Perhaps you could put in a screen 'window' on each side of the pop-top fabric. This would definitely help with cooking heat generation, as well as be a relief from summer heat and stuffiness. But installing a vent fan should be helpful as well, until you get around to screen installation. Sounds like you like to cook, assuming that pot of chili was started from scratch and not from a can!
I don't think you'd need to remove the pop-top fabric to put in screens. If you made cut-outs and glued on your 'windows', that would be so much easier than taking off the pop-top fabric.