I have fine hair, but my boyfriend has extremely thick 4a hair that I usually press before he gets it braided because it's too much for the braiders to handle!
When I get done with his hair, it looks like a relaxer and swings. The key, I've found, to getting his hair not to be poufy was to find the right amount of heat. A too low temperature on his thick thick hair just did not work. I was used to dealing with my own hair and my hair can't take half the heat his can without burning off. I also use grease and I put it on his hair wet. Becasue he has so much hair, it does not weigh it down too much and make it scraggly and since it is wet when it is put on, it doesn't feel greasy either.
I also agree to work in a well-ventilated room. When I press my hair, that's my main problem. Plus, I'm also nervous that I'm gonna burn myself so that makes me even more hot. Go ahead and even make the room cold, you prob wont be cold for long!
Oh and one more thing, sometimes I'll use Kemi-Oyl after pressing to smooth my hair down when I've done a less than stellar press job. It works well for that on my head, and may for yours, too.