The most probable cause of a hot start is late ignition.
The most probable cause of a hot start is low battery or a weak starter. Too low an operating RPM at the time fuel and ignition are introduced tend to lead to a start going hot. The primary reason is that the engine isn't turning at a high enough RPM, and has insufficient fuel flow.
While minimum RPM's are provided for the introduction of fuel during the start sequence (movement of the condition or fuel lever, depending on your installation), one is always smarter to wait until the engine has reached it's maximum motoring RPM during the start sequence before introducing fuel.
Will an engine actually start during a hot start sequence? You should never find out, and it's irrelevant. If the engine has gone hot, it needs to be shut down. If it's approaching start limits, then fuel should be cut off and the engine motored...then started normally if possible, to stabilize internal temperatures. If the engine exceeded limits, it should be cut off, motored to cool, and shut down....and not run again until inspected.
What you should not do is let the start continue if the engine has gone hot. This is a critical condition, and as far as you should be concerned, marks the end of the life of that engine during the time you'll be operating it. Don't let the engine approach a takeoff limiting temperature setting and do nothing. When you see temperatures accelerating rapidly, cut off that engine immediately. If you see temperatures approaching limits, cut off that engine immediately. Don't let it exceed temp limits in the first place.
Causes for hot starts can be several; bleed failures, certain reference line failures, fuel control problems, case drain failures, poor starter, early introduction of fuel, low battery, damaged compressor, inlet blockage, etc.
The damage that can be done from an engine going hot won't be readily apparent, but can be excessive,and can lead to a catastrophic failure.
Not all engines, or even all dash numbers of engines use the same thermocouple placement. While an engine may appear okay, the actual temperatures inside may be far hotter in other areas of the engine where temperature monitoring is not taking place, and where temperatures normally don't become a problem. This is the case with a hung start, when the engine can be cooking farther upstream from the thermocouples. The engine may not appear to be getting that warm, but it may in fact be burning up upstream from the thermocouples, with in sufficient heat getting to the thermocouples early enough to warn you. Your only warning may be acceleration stagnation, and there are a number of reasons that the engine can reach a hung start condition.
A milking start - Turning the fuel on and off to control temperature is a NO NO!
Depends on the engine. I operated a -45R for some time in which it was absolutely necessary. It's a common requirement in some engines, particularly some C250 engines at higher density altitudes. Some engines do fair better, and have a longer life, or simply require an operator-modulated start. I've never had to do it on a -67 that I can recall, but others, yes.
Have you ever actually had a hot start?
Absolutely. And hung starts. Pay close attention to the engine instrumentation during the start. What you miss or don't address during the start could very easily come back to bite you, or someone else later, during takeoff or in flight.