The question is somehow similar to Can I use LGA775 heatsink on LGA1156 CPU? although I didn't quite get the answer and the point might be a bit different.
I don't have the stock cooler for the 1155 processor, and have a 775 stock cooler that works just fine. I have a motherboard that seems to have the holes for both 775 and 1155.
What I want to ask, if I manage to stick correctly this heatsink, will it work fine or will it have some thermal problems? (because the coolers might be different)
edit: on a side note, I have seen that the 755 P4 3.0ghz TDP is bigger than my present CPU (84 W against 69W). I dunno if this means much though.