Sticking throttle plate, sticking throttle cable, incorrect ignition timing, incorrect idle speed, air leak. Worth checking them all!
Hot start issue is worth checking the starter and associated wiring. Cable resistance increases with temperature, but not significantly - so I'd bet on a dodgy connection or knackered starter/solenoid. Cold start requires more torque from the starter and thus draws worst-case current from the battery, so a weak battery usually shows up as a cold start issue.