That's a tricky one Anglaise, I've found that running in the heat leaves me disproportionately wiped out the next day and that's running at a slowish easy pace so I'd be worried about the impact on my health / immune system if I had to push myself.
Wrt stomach problems do you find that the likelihood or severity increases in line with the length of the run?
If so could it be related to the length of time that the gut is 'shut down' (because with high intensity exercise most of the blood supply is needed for the working muscles and so is diverted away from the viscera) ?