A hot start is, I believe, when it is very hot outside.  I've often heard to starting an engine in January as a "cold start", so I'm assuming it's the same the other way around.

Then again, come to think of it, this is probably completely wrong since it doesn't make any sense.  Hurray for those of us who just made an ass of themselves!

A hot start is when the engine ignites and reaches self-sustaining RPM, but the combusiton itself is unstable and the exhaust temperature (EGT) rises rapidly past its max. limit.

A hot start can happen if you add too much fuel during start up (throttles aren't at idle), air intake/exhaust are blocked.
But a hotstart can even happen when starting the engines in sever tailwind, which causes the compressor to run backwards.

A hot start is basically when you introduce fuel before you have enough air for cooling and combustion.  Its like spraying fuel into your combustion liner and then lighting it, and well, burning it to crisp.  It can happen in any temperature pretty much