I never thought of the temp gun- I have one too!!! Need numbers to compare it too. Yes, regearing lower will reduce loads and make your clutch's life easier. Given your current setup, I doubt you'll be able to fit a much larger rear sprocket without clearance issues. You will likely have to set up a jackshaft. This is an intermediate shaft on bearings that hold a couple sprockets. Your clutch chain-drives the shaft with one sprocket, in turn the second sprocket drives your axle. Ultimately, you end up with two chain runs, and the ability to gear down much lower than you could without. As an example, My kids' cart is geared at about 16:1 as I recall. To do this without a jackshaft would require a 160 tooth rear sprocket! The wheels wouldn't touch the ground!
EDIT- Just checked- 10T clutch to 32T on jackshaft, then 12T on jackshaft to 60T on rear sprocket for a final ratio of 16:1 reduction. (10/32 x 12/60=16) This keeps the kart slow and controllable while they're learning not to crash into things. Absolute (*&^loads of torque, tho'!
While this is likely a far too low ratio for you, I think it should give you an idea...
Cheers- Chris