Welcome to the 'club, sorry to hear about your problems. It sounds like the PO left that car sitting for a while, you'll be chasing down a few gremlins. IMHO BMWs have a few well known problems that get worse if they sit still for too long.
TL;DR: I ended up buying a cheap HF radiator pressure tester. It's pretty easy to find pressure leaks with that tool, you can actually hear them. It's not perfect - I don't like the manual air pump, can't hook it up to a compressor, but it's only like $80 all in, comes with a decent set of pressure adapter caps too.
My E30 ran uncomfortably warm for years, at 3/4. I did a lot of work to track it down. Did the hose delete mod, didn't help. Two new coolant manifolds (make sure you avoid the cheap URO junk). New low-temp thermostat, new fanstat, new aux fan & resistor, new clutch fan. Still overheating.
But then it started the 'creeping' temperature rise too, touching the red zone even at highway speeds. I parked it until I could figure that out.
The pressure tester immediately found several leaks. Heater core was really bad. The radiator expansion tank seals were also leaking. I didn't have any of the 'normal' M42 problems...water pump, radiator & expansion tank were all OK. Swapped out the heater, core, no more overheating. The car started acting normal after that, so I swapped back to the normal thermostat & fanstat. Quick warm-up, temp needle reliably just under 1/2.
Topic: E36 M42 Overheating,Everything changed PLEASE HELP (Read 2974 times)