I have a hardcase and love it. Very inexpensive, but has already protected against at least one injury.
In terms of heat dissipation, in informal tests with my unit, there were no noticeable differences between using it and having it off. However, I am a light to medium user (intense activity but for short periods). If you plan to game on it all day, I think you will see a difference, and may want to keep the hard case off.
When carrying it around I use a Booq Mamba bag. It is wonderful, and negates the need for a sleeve.