Upside of not running a cover with an automatic is that the converter spinning creates quite the wind in the bellhousing.
No cover means that wind is constantly being refreshed with cooler air removing heat from the converter, bell housing, and back of the motor.
Downside is a little more dust gets in there.
When dust gets in there the first place it collects is right where the pump seal rubber contacts the converter snout and can wear the seal lip sooner.
It's a trade off.
A clutch will also will run hotter with a cover, but a clutch is more susceptible to contamination of dust, water, rocks and such.
I have seen manuals and autos both with damaged bell housings from rocks getting thrown up in there, so that part is the same between the two.
