I am somewhat reluctant to go along with what appears to be the accepted idea that heat has built up causing a hard start after a shut down. I AM not saying this is not possible but a few things make me want to say something else is happening here.

I experienced hard starting after a hot shut down on several old cars back in the 70's.  When I say hard starting, I mean slow cranking like the battery is nearly dead, or timing is over-advanced.  I would have to wait awhile for things to cool down, then it would start up fine.  I think the starter motor got over heated.  That's why GM installed shields around the starter motor.

I have heat issues as well. Not when normal driving then i run 180-190 but on race days when i push her im always around 220 obviously worse through out the day. My solution is going to be to ditch the old mechanical fan and install an electric pull type fan. On race days though I also open the hood after every run and use a pump type pestiside spreader full of water to mist my engine compartment, I also run with my headlights up to allow more airflow to the radiator. Our C3s will always have heat issues due to poor design for cooling. There is something like 3 foot of fiberglass nose and the like in front of the radiator not to mention the headlights hanging right in the way of airflow

Since the Shark is a bottom breather, the headlites really don't impede the airflow that much.  Overheating can be caused by a radiator that needs rodding out, missing foam seals, missing fan shroud, bad fan clutch, bad t-stat, collapsed hoses, not using a 50/50 coolant mix, and air trapped in the engine.

Hard hot starts can be caused by timing which can be worked around by putting a switch in the coil supply (non-HEI) and spinning the motor and then turn on the coil.