A major problem with the Bmw E34/E32 especially the BMW M30 3.5l out of the 535i: overheating.
Don't expect the headgasket to last long in these conditions.
The temperature needle should be at the 1/2 mark all the time. If the needle is near the 3/4 mark or red area, you have an overheating problem, fix it soon.

On the BMW E34 525i 92 on and the E36 325i/is with M50 engine, the engines were fitted with plastic impellers waterpumps. These waterpumps fails, the impeller desintegrates and you are left with no waterpump at all... the engine overheats. You need to check that you have a waterpump with metal impeller. Change your waterpump ASAP if yours has a plastic impeller.

Understanding the cooling system:
• The waterpump (centrifugal type) is driven by a belt. It allows the coolant to circulate.
• The thermostat controls the coolant flow into the radiator. Closed when the engine is cold (nothing goes in the radiator, open when the engine gets warm to flow the coolant inside the radiator and cool it down.
• The primary coolant fan is mounted to the front of the waterpump with the fan clutch.
• The fan clutch is a viscous fluid type that control the speed of the fan based on engine compartment.
• A two speed auxiliary cooling fan is mounted in front of the condenser. It is uses when the A/C operates and when coolant temperature exceeds 196F (91C)
• The fan shroud is also an important item not to overlook: the presence of a shroud, with about 1/2" to 3/4" clearance between the tips of the fan blades & the shroud opening, and the fan inserted about 1/2 way into the shroud opening is essential for efficient cooling performance.

First: make sure that your radiator is in good condition, check the belts, the hoses and the coolant level. Make sure that there is no coolant leaks. Check the condition of the shroud for cracks & its proper installation.

Car fluid or coolant circuit element just changed:
Your overheating is probably due to air trapped into the coolant circuit. Use the bleed screw to bleed the circuit. Then bleed again, again, again and again.

Nothing had been changed, car is overheating while idling or heavy traffic:
1. Check that the thermostat works and opens.
2. Check the fan clutch.

Car overheating while driving. Not stop and go.
1. Bleed the cooling circuit.
2. Check the thermostat.
3. Check the water pump.
4. On the 535i, check the bypass hose located and attached just above the upper hose neck on radiator and runs along the inner walls to the Resivior tank. If it is plugged, the car will overheat.

Overheating with A/C on, or very high temperature only.
1. Check that the auxiliary fan is working properly(Bentley manual page 170-4).
2. Check the fan clutch.

How to check the thermostat:
A slow working thermostat is hard to diagnose. When the engine is warming up and the temperature needle is near center, touch the top radiator hose. If hot, the thermostat is working (could still be a slow one). If there is cold area in the hose or radiator, check the thermostat.

How to test the fan clutch:
Sorry guys, the newspaper test is not reliable. If the thermostat doesn't work or is slow moving, the fan clutch will fail the newspaper test and will spin freely don't even bother explaining how it is done as it is dangerous.
What you should do:
1) make sure that the thermostat is working!
2) when the car is cold, the fan clutch should turn with a small resistance and not spin freely.
3) Let the car idling and the hood not closed but down. After 5-10 min, the temperature will rise at the 1/2 mark, check that the fan is blowing a LOT of air inside the engine compartment and increase in noise level, no need to put your hands, you will feel it. If when the temperature hits the 3/4 mark, the fan is not blowing a lot of air, that means that: either the thermostat is not working or slow, or the fan clutch is bad.

Bypass hose modification: (Thanks to Dave Smith) Picture from Gale
Dave enlarged the hole on the end of the pipe from the radiator to the expansion tank.

The pipe that runs from the radiator to the expansion tank is about 1/4 inch diameter (internal) , but just as it enters the expansion tank it reduces in size down to 1/64 inch diameter. this pin hole is what was blocking and causing overheating... I have enlarged the hole by running a 1/4 drill down the pipe and this should prevent any futher blockage.

Great Overheating write up from Arnold Matusz.
The interesting thing about how this all began is that I gave my car for a little test drive to a friend who normally drives like crazy.
When I drove the car everything seemed allright, but when he gave me the key and I got into the car, the engine coolant was so hot that it would probably have bent the water indicator needle in my dashboard. First I thought he really stood on the gaspedal instead of "on the seat" and thought it needed a little cooling down time! But it was really aukward because an engine should cool itself down at 600RPM and 6000RPM aswell!

I waited a bit for it to settle down but it didn't help much as I've turned the engine on ... it immediately boiled the water. So it was clear that the coolant system had a bug (thermostat, not enough coolant, headgasket, waterpump ...)
As my dad is a car mechanic he immediately spotted that the thermostat was blocked in a closed position. This normally prevents the water to flush through the radiator so that the engine can't cool itself down!
To change the radiator you only have to remove the thermostat housing (if you can get hold of the little seal in the housing do it, it's worth it) replace the thermostat and put back the housing. Don't forget to clean the surface so the housing can close 100% on the head ... to prevent any water leaks.
After all these have been done we noticed how difficult it is to bleed the coolant system! It was impossible not difficult! The engine was still overheating, now we thought the reason was that the thermostat is closed, there's not enough water around it (air trapped inside the system) and this is why the engine is overheating. But the thermostat was working just fine.
Then we suspected taht the headgasket had some crack and that part of the compressed air-fuel mixture from the cylinder is escaping through the crack into the coolant system! It was pretty viable as the engine overheated a few times! So we changed that aswell!
But when we got back to fill up the coolant system with coolant ... it still didn't want to bleed itself through.
The interesting part is that the engine could be cooled down if you use the heater in the car. The radiator from the heating system acts almost as the normal radiator, it blows loads of hot air into the cabin thus cooling the engine down!
The next step was to change the water pump, although it didn't seem a very viable solution, as it gave a no good explanation why there is heating in the system!
When we took out the water pump the PLASTIC IMPELLER remained inside the head. That's when we got really happy as we found the reason for the whole overheating problem!

Overheating troubleshooting!
0 - check coolant level
1 - check if thermostat works
2 - headgasket replacement
3 - water pump replacement
4 - check the head for cracks

BUT if you've got BMW M50 (525i after 89) engine the order is a bit changed! (these models tend to have a plastic impeller on the water pump which suddenly walls down from the shat that should drive it ... so you actually end up with water not moving around at all in the egine - thus the extremely rapid overheating)
0 - check coolant level
1 - check if thermostat works
2 - check the waterpump
3 - check the fan clutch
4 - check the cooling fans for the radiator
5 - replace headgasket
6 - check the head for cracks
7 - replace engine if all these won't work :P

CAUTION: when you mount the new thermostat handle the thermostat housing with allot of precaution because it can easily crack and you end if with a leak (where not only water escapes but the engine can get air inside the coolant system which is a bag factor when it comes to overheating).
When working on your coolant system and you are buying parts: always ask for a metal impeller water pump, and procure a metal thermostat housing).

IDEA: if the water pump is at faul you might cool your engine down by turning on the heater in the car ... This will let you drive it to the services, better than walking / paying for a trailer! It worked for me:)