I'm fairly well in agreement with LPC1625 on this subject. I like the pistol in the same location (3 o'clock for me) where it's usually worn. But jogging is one of the few times when I switch to a smaller piece.
I put a wide gunbelt on over my underwear, then pull on a pair of loose shorts/jogging pants, and tighten the drawstring. At this point the grip is exposed above my waistline. I cover it with a loose and untucked t-shirt or sweatshirt. It's easy to access with one hand.
I carry a S&W Airweight .38 +P, and hardly know it's there. I'm sure the LCP's, KelTecs, and others would all work great. I can hide a larger pistol under a sweatshirt, but there's more bouncing and adjusting.
For night-jogging, I also carry a small flashlight in my off-hand. Nothing 'tactical', just a small light with a good beam that can be clicked on with my left hand. I consider it as important as the pistol. You have to be able to see your target, and be certain it presents a genuine threat.
Good luck with the jogging, and let's hope this heat goes away and makes it a little more pleasant.