Thermal compound or thermal paste is a material that is used to enhance the surface heat transfer from the CPU to the radiator fins that the fan is blowing cooler air over to keep the CPU cool. I would say that the paste or thermal compound isn't likely bad but it can dry up and does benefit from being re-applied after both surfaces are cleaned properly. There are lots of great You-tube videos available to tutor you on this process. In regards to a new case for air flow it's hard for me to guide you as I don't really have a great overall view of your case now and I don't know what kind of budget you have. When you add up a case, some fans, new thermal paste and your time and energy for a few hundred more you may be able to get a whole new rig. I would think about where you want to take this hobby and if you see yourself wanting to learn more and be very hands on then invest in a great case and PSU by a premier manufacturer. Then transfer what you have over and when your wallet recovers then look into a new mobo, CPU, ram and graphics card if you are so compelled.