I am using a Tony Miller Vegan strop, and the amount of draw I get on the vegan leather side is amazing. It takes a bit to get used to, but there is an appreciable amount of resistance when you are stropping a razor. You really have to use light pressure.
One time I was stropping fairly quickly, and I noticed that the razor got quite warm. It was not just where I was holding it, but the entire blade was noticeable heating up the more I stropped. I though I was crazy at first, so I brought it over to my girlfriend and said "feel this, is it hot??", and she indeed felt the heat too. So there is definitely a correlation between amount of draw and heating up the razor. This really isn't surprising to me since draw is typically defined as the amount of resistance there is during stropping. Resistance is nothing more than friction on the strop, so you're basically giving your razor rug burn. :p Now whether the amount of heat has any direct effect on the quality of the stropping is something that I haven't experimented with, but I would be suprised if it didn't have some connection. I would think the heat would only help with the stropping action, since the metal would be more malleable.