Some of the new air brush compressors have a built in on off pressure switch. When you press the airbrush trigger the compressor turns on. Once the pressure switch sences the back pressure from the airbrush trigger no longer being depressed, the compressor shuts back off. But... in all honesty it sounds like a better choice for you would be a compressor with an attached air tank, as the prementioned could still have over heating issues if runconstantly. A compressor with an attached air tank would allow for a storage of air and should have a higher cfm rating allowing them to keep up with a low pressure device like an air brush. The only draw back to a unit such as that is added cost of the compressor, a bit more noise, and you will need a regulator to lower the output air pressure for use with the air brush. You need to look for one with a 6 to 8 gallon storage tank, and something with about 1.5 to 5 cfm at at least 90 psi to keep up with your airbrush. A compressor like that could have plenty of other uses around the house as well and should cure your over heating problems.

Here is a link to Badgers Air Brush Compressor with the trigger activated start stop. This is on my to get list personaly.  ;D   http://www.badgerairbrush.com/Images/Compressors/compressorcatalog-3.jpg

And here is a compressor with a built in air tank.something like this Hitachi would work well for what your doing, but you will need adapters, quick disconnects, and an air regulator preferably one with a gauge. And they are not quiet, though they can be more useful around the house.

http://www.lowes.com/pd_368388-67702-EC510_4294795218__?productId=3550670&Ns=p_product_qty_sales_dollar|1