I know that engine oil will get warmer w/o the car In motion .
But does automatic transmission oil get warmer if the motor is running but the trans is in park ( or neutral)

As the gears are not moving ?

Yes. Even though your gears aren't moving, there are still moving parts in there while the engine is running. Most cars I know with an automatic transmission route a fluid line from the transmission to the radiator to warm it up or cool it under load.

Mainly when driving and especially if under load.
It is why transmission fluid gets routed through the radiator or a transmission cooler on many vehicles.
I installed a stand alone cooler on my truck to bypass the radiator.
It can be a big problem if later on the radiator life there is corrosion and radiator fluid and transmission mix.
Towing is especially taxing on the heat issue.

The only thing moving in an auto transmission in park is the torque converter, the pump and clutch drums but clutches have no apply pressure, the output is "locked" mechanically.

In Neutral, the same thing but the output is not locked, so the car could be pushed or roll on an incline, but effectively the same thing occurs in the fluid circuit so the car does not move.

Fluid will warm, but never as much as in any gear and and if started and not driving, the fluid temp will only reach minimal temp.

A transmission in gear with the parking brake set will result in elevated temp due to the stall of the converter having the impeller working against the stator being held in place by the brakes and the torque working back through the gear train against the converter so the converter will heat up the fluid.

Main things affecting fluid temp in order of highest to lowest contributing- converter operation, pump operation, gear train friction, very short intervals when clutches apply and un-apply and the band(s) apply/un-apply (clutch plates, steel plates and band(s) generate heat, and the fluid absorbs that heat) and fluid flow through the lube circuit.

Converters create a lot of heat in the fluid due to fluid friction against the impeller and stator blades and more in neutral and park, as well as high throttle settings as the converter is "slipping". A lock up converter has an internal clutch in the converter that engages and makes the converter operate as a mechanical single unit and no internal friction occurs when locked up, and 100% power is transmitted to the input shat of the transmission.

Automatic transmissions do heat up while idling.

In fact, some transmissions can overheat from excessive idling in park. The fluid isn't circulating much (if at all) while in park, and there's no airflow to aid in cooling either.

This is an issue that some cops driving off-the-shelf undercover/unmarked vehicles run into. They'll idle for a long while (i.e. hours - such as while performing surveillance), and then when they try to drive off, the transmission is hot and starts slipping and hesitating. Not a good feeling when you've been staking out a location for hours, the bad guy finally exits the building and takes off in their car, and you're trying to follow but your car starts acting up.

There are often kits that can be installed to alleviate this by adding additional active cooling and/or circulating additional fluid in park. Or you can potentially shift the car into neutral and set the parking brake, then let it idle in neutral, which on some models helps by circulating more fluid than in park.

Thanks a bunch from taking the time to share.
It's appreciated

quote:

But does automatic transmission oil get warmer if the motor is running but the trans is in park ( or neutral)

Yes, because fluid is always flowing. The transmission's fluid pump is connected to the engine's crankshaft via the flywheel and torque converter, so it turns at the speed of the engine. It is also a positive displacement pump, i.e., what goes in must come out. At long duration traffic signals I also like to shift the transmission to neutral, as leaving it in drive all the time also heats up fluid.

Heating fluid at idle in gear at traffic lights, poses no wear and the temp is not going to increase to any significance, but the forward drum applying/un-applying results in the most wear the clutch ever sees.

If you want to see how fast fluid flows, leave a cooler line off or loose and start the engine. Don't ask me how I know this.

Yeah. Aircraft hydraulic systems. (F-15E 86-0185)

I have seen what a mess 53 GPM at 3000 PSI looks like when a PC1 system supply line splits during full after burner run in the hush house.

I'll tell you, even if you don't ask.

Very little heat is generated by the transmission sitting still with the engine running.
Almost all is from the heat transferred through the common body of the heat exchanger (radiator).