I was having that problem with the 360 in my Cuda. It may be a different issue for you, but for me, it wasn't the starter at all. I had replaced the stock fan with an electric, and I found that I had wired the electric fan in a way so that if the engine was warm, the fan would be running while I was cranking the engine. The draw that the electric fan had was enough so that the starter hardly turned the engine over. Once the engine cooled enough, the fan wouldn't run anymore, and the engine would start fine.

I ended up rewiring the electric fan so that it will only run when the key is in the run position, and will not run when the key is in the start position. No starting problems anymore.

It is most likely what the others are saying - heat soaked starter or starter relay, but it's fairly easy (and free) to check to see if something else is using electrical power when your key is in the start position - fan, stereo, etc. If you pull the neutral safety wire (or ground wire if you have it rigged that way) off of your starter relay, you can turn the key to the start position and the engine won't try to turn over. You can then see if anything else electrical is running while the key is in the start position. If not, I'd think it's a heat soak issue. and try a heat shield for the starter to see if that helps.