The airfilter is intended for cars and trucks.....you really don't need one on an airplane. It wouldn't hurt but it's certainly not going to remedy your situation.

Take the cowling off so you can work on your engine. You'll need to adjust your low end needle valve, and you'll need to be able to pinch the fuel line while idling to assist in determining this adjustment.

How hot is the engine after it's ran for a few minutes and died? How hard is it to restart?