Dies at idle

I have a 83 southwind with a 351. The boat runs Awsome until it is run pretty hard for about 20-30 min. It runs good above 1000 rpms and accelerates and everything well. The problem is at idle and mainly at idle speeds when in gear. It wants to miss a beat and die. It will start back up no problem, don’t even have to give it gas. But as soon as I put it back in gear it tries to die. It does not do thst until it’s been driven a while then just gets worse and worse the longer I drive it but at higher speeds it does perfectly. I was wondering what could be happening to cause this? The motor runs right at 150-160 but I can feel the carb and air filter getting pretty hot and wonder if it’s getting to warm with the hood down. I feel it has to be a carb issue