Hi Johann
I'm not an expert on the P-47. It did have cockpit heating, cooling, and defogging controls. For specific answers to performance questions, try the Aces High website. You will find graphs and charts that show climb performance as well as folks that can help with your questions. Try the Aircraft and Vehicles Forum:
http://www.hitechcreations.com/ubbframe.html It is difficult to stay in a good firing position when chasing a plane that is being flown well. The gun attack is very complex and the target does not have to do much to spoil the attacker's aim.
The attacking pilot must have a good maneuvering aircraft and he must be proficient in BFM. If either is missing, then the attacker's ability to stay behind the target is going to be much harder. Here's a rough estimation...if the attacker's airplane is inferior in performance to the target aircraft, then the attacker needs to be at least as good as the defending pilot...and perhaps even better in BFM if the attacker is going to win. Conversely, if the attacker has a better aircraft, then he may be able to win even if his BFM skills were less than his opponent's.
Andy