You could try putting a pair of underwear on over the diaper, just make sure the underwear aren't too big, and you shouldn't have to worry about him getting too hot. If that doesn't work, I second the idea of putting the diaper on backwards and/or using duct tape.
As far as potty training goes, I am a firm believer in John Rosemond's 3 day, $75 theory. It goes something like this. Bring the child's potty chair into the middle of the room where he is. Remember, children this age have very short attention spans and a potty out of sight is out of mind. Take the diaper or pull-up off the child and put him in underwear, with no other pants. Don't use the 5-ply super absorbant underwear, just regular underwear, and expect accidents. When he pees, it will feel cold, wet, and run down his leg and hopefully he will think it is yucky and uncomfortable. When that happens, don't scold, just say something like, "Uh-oh, you had an accident. You should have peed in the potty, huh? Next time you need to pee, tell me and I'll help you pee in the potty." He will have lots of accidents, but don't give up! It may take longer than 3 days, but unless his developmental issues get in the way, he will get it. The $75 is to have your carpet cleaned once he is trained. This worked on both my kids. My daughter was trained a week before she turned 2 and my difficult child son was 2 yrs 5 mos. Both took about a week. I tried earlier with-my son, but he wanted nothing to do with the underwear and would throw a fit if I tried to put it on him. I kept trying every month or so and all of a sudden, he thought underwear were great! As a side note, in my opinion it is worthless to try to potty train a child who is wearing a diaper or pull-up. They have no reason to quit peeing in it. Just my opinion, for what it's worth.
Not to discourage you, but while potty training should keep him from peeing everywhere (maybe not) it may increase his facination with his boy parts. Let's hope not and good luck!