well if the exhaust fan on the psu isn't turning at all vs a one that is spinning like it should, there might be some minute difference in the air temperature inside the case which will show up in the gpu temp as well. Also the psu itself will get hotter when pushed to the limit...
Other than that, nope...
The purpose of the fan on a psu is to protect the psu from overheating, not to help case cooling. On the best quality gold rated psu's, the fan may not even operate at all.
With that in mind, an underpowered psu feverishly trying to keep itself cool might actually help your case cooling!
Graphics cards do run hot, particularly older gen cards. But, they are built to do so.
I would not worry too much about it unless you are getting overheating related failures.
The best way to attack overheating is to look at case cooling. Take off the side covers of your case, and direct a house fan at the insides. If your temperatures improve significantly, then you have a case cooling issue. A good cooling case replacement is <$50.