He may be on the brakes while he is driving or over trail braking. Get into the habit of grabbing the axle in the center, if its to hot to hold or even burns you that is the case. Keep working with the driver to break that habit. Keep grabbing the axle till you can start getting close to the disc without pain.

It sounds like the caliper is not releasing. Check the adjustment of the rod between the pedal and master cylinder. Make sure the rod is adjusted properly and allows the lever on the master cylinder to come all the way into the release position.

Brian

If the brakes are ok when it’s cool the linkage is good. It sounds like you’ve still got air in the system or it’s leaking in during the track session.

Gif

Walt  The clearance between the pads and caliper is less when the brakes heat up. If the rod is adjusted to tight then you may have clearance when the brakes are cold but no clearance when they heat up. Then they drag and get  hotter and close even more.

Brian

Your caliper pistons and seals are most likely full of corrosion and build up.

look at the pistons closely before any amount of brake pedal is applied, look at the distance the caliper pistons are at.

Drive the kart and get it to act up, then look at the distance and see how much further the pistons are sticking out

I almost wanna put money down that your calipers and master cylinders are in need of rebuilding, or a good honing and cleaning.

Try duplicating the problem, as I suggested first, paying close attention to the calipers first, if you confirm that the pistons are not returning, then take the calipers apart, and master cylinder, and rebuild them, flush and bleed them, and good to go.