Rapid overheating under certain conditions (M42)

[pentiumbased]

1994 318i M42 211000km. Had the car for little over a month, it's my first car.

One day i was stopped on my driveway, facing uphill, letting the torque converter hold the car up against gravity for about a minute. The temp shot up and I put it into neutral, and it went back down again.

Several days later I did the same thing in traffic, letting the autobox keep the car from rolling back, and it happened again. Luckily I got moving soon after and the temp went down.

It has happened at least another few times but my memory shuts off during working and commuting hours so I'm short on details, sorry. But it seems the problem only occurs when the engine is at very low speed under slight load. Which sounds like it should happen anytime the car is in drive but stopped. But I've sat in bad traffic with the AC on&off nearly every day and never had an issue. Worth noting however that my AC hardly works.
On one occasion I recall going into neutral but the temp continued to climb. It hit the red and I shut the car off. I relighted the engine after about thirty seconds and the temp fell back to normal after about 15s of idling.

Today I tried to intentionally recreate the problem. Facing downhill and preparing to reverse into my driveway, I popped the hood latch and let the trans keep the car from rolling for about 20 seconds, and the temp shot up. I quickly got into my driveway and put the car in park, and I looked under the hood to see that nothing was amiss, but I should have had something soft on had to stick into the fan to see if the clutch was engaged. I got back into the car right as it went into the red and I shut the engine. After restarting, the temp went back to normal.

I'm going to check fuses and aux fan relays this weekend. Hopefully this overheating issue does not get worse before then, and it as well as my ABS light can be solved with new relays. But for now I would like some advice so I can get a head start on the cat-and-mouse game if it comes to it. Water pump and rad hoses are recent according the service history and coolant looks good.

EDIT: What the hell? I don't have an aux fan apparently. I wonder where it is now. It's certainly not on the car.
Also, I've been able to recreate the problem most reliably when reversing under any conditions. The temp shoots up as soon as I go into R and it will keep going up unless I shut off the engine.

[Eric93se]

Never let the engine go into the red, that's overheating it. I'm surprised the wp is new, but do the thermostat and the rest of the cooling system. wp is cheap you should just do the whole cooling system. You should start doing basic drain/fills for the trans, do it once a year and use quality synthetic, if the current oil is not bright red then do it a second time a few weeks later. Be sure to read up on how to do it properly, I'm not familiar with your trans but on the 4L30E the engine has to be brought up to temp and the car has to be raised LEVEL (I put a bubble level on the trans pan).

Only buy quality brands when doing the cooling system, Behr, mahle, beck arnley, OEM bmw. do not buy URO or Moto* or SKP.

[pentiumbased]

Never let the engine go into the red, that's overheating it. I'm surprised the wp is new, but do the thermostat and the rest of the cooling system. wp is cheap you should just do the whole cooling system. You should start doing basic drain/fills for the trans, do it once a year and use quality synthetic, if the current oil is not bright red then do it a second time a few weeks later. Be sure to read up on how to do it properly, I'm not familiar with your trans but on the 4L30E the engine has to be brought up to temp and the car has to be raised LEVEL (I put a bubble level on the trans pan).

Only buy quality brands when doing the cooling system, Behr, mahle, beck arnley, OEM bmw. do not buy URO or Moto* or SKP.

I hope the 90s total I've had the engine running above the 1-o-clock position on the temp dial has not caused any damage.
The trans fluid is good as I topped it up due to a trans cooler leak and it was weeping red fluid to begin with, probably bc it was at an auto trans shop circa 2017 according to carfax. Manual swap is currently sitting under tarp.
My car does have a 4L30E (as all e36s do I think). I filled the trans after running thru the gears on jackstands, I was missing almost 2L in the end

In any case I don't see how the auto trans could affect the functioning of the cooling system. I considered some kind of weird 1-in-10000 wiring gremlin. But with no aux fan there's nothing electronically controlled in the cooling system.
I just checked the service history again (actually half parts receipts bc the owner before last did mostly DIY i assume) and the thermostat and bleeder screw are also recent, so those are ruled out.
I'm still wondering where on earth did my aux fan go.