Full towers are definitely a great way to go for preventing heat issues. If you have the space, find one and use it. If you're looking for LAN party portability, that creates a whole different issue. Don't be afraid to repurpose older towers either. A 20 year old box that has the right screw hole configuration is fine.
If you're going to do the TB drives, try to get matching pairs if you can and run them in RAID 1. Also, running a pair for the OS and a seperate pair for the data is a good idea as well if you can swing it. This will help eliminate issues that crashing games might cause. And speaking of games, if you can do a single 3GB video card, you might look into a pair of cheaper, earlier versions since GeForce cards run better as a pair than they do as singles.
Back to the original question, look around for a cheap used full tower if you can afford the footprint. Otherwise, make sure that any mid-size you look at has the power supply on the bottom and the drives on top with either a larger vent on the top of the same or a good set of fan grills towards the back. And don't be afraid to modify the air flow in any case. A couple pieces of cheap cardboard can make the air move where you want it and keep things cooler by directing heat one way and keeping components from heating each other.