(2nd part):
Let's now assume that the meat was left out of the fridge for quite some time (at 'warm' room temperature) before cooking. In this case the bacteria already on the meat (plus others which might be picked up from the air or the surface on which the meat was placed) will multiply rapidly. Although the cooking process will kill off many of the bacteria there are going to be two problems when you come to eat it. Firstly, since there were more bacteria on the meat prior to cooking than there ought to have been, more are going to survive the cooking process but, even it was possible to kill all of the bacteria during cooking, the meat still wouldn't be safe to eat. This is because food poisoning is often caused, not directly by bacteria, but by the poisonous waste products of bacteria. All of the bacteria which were multiplying when the food was left out for too long were creating chemical poisons. Cooking might kill most of the bacteria but it won't remove the toxins left behind which can lead to food poisoning.
So, please note, in the above case, the bacteria were not multiplying either when the meat was hot or when it was cooling down. The damage was done much earlier.
Lastly, let's assume that that the meat is cooked straight from the fridge but then left out at room temperature. In this case, the freshly cooked meat is fairly free of bacteria (although some will have survived cooking) and it won't have toxins caused by bacteria (because it hasn't been through a 'warm' phase). Because it's then left out in 'warm' conditions, however, those bacteria which survived cooking (plus other bacteria from the air and from the surface which the meat is placed on) will then start to multiply and create more toxins. If the meat is now eaten cold, both the bacteria and toxins will be present. Even if it is re-heated, the bacteria may be largely destroyed, but the toxins will remain present.
Chris