This is a case of theory vs. real-life experience. Yes, if you want to err on the side of caution, then never eat anything left at a cool/high temp over 20 minutes. Real-life experience tells us that is over-board and we are wasting perfectly good food. Today, I played golf with Mr Bee - at the turn we both got cups of salad - tuna for me, chicken for him. I could not eat all of mine, delicious as it was. I brought the leftovers home and it is now in the fridge for tomorrow's lunch. I have done this before with no problems.
The notion of bacteria doubling, tripling, etc., is scary, but what does it actually mean? Does the presence of bacteria automatically mean poison? Isn't bacteria present in everything we eat already? Some good/some bad?