Have you thought about going to the Apple store and seeing if they will upgrade your system with the Apple (or third party) SSD unit or doing it your self (leaving the HD alone)? I would recommend that first, while being a bit more expensive adding in the SSD option has its benefits creating a fusion drive. Here's the IFIXIT guide for Apple SSD option.
If that is not an option then replacing your HD with a SSD will be tricky here. Yes, you do have the fan issue to deal with but the bigger issue is getting the drive to fit. The problem here is the HD is a 3'5" drive and the SSD is typically 2.5" (without any added case). Review this IFIXIT guide HD Replacement guide. Consider the adapters you will need here and how the cable harness will need to be routed (not much slack).