No chalk or talcum powder? 'Could be chafing, or a wrinkle in the tube, though if that was the cause, it should be evident upon disassembly. I've had two flats in one wheel on one of my planes in the last year, having never had a flat mainwheel before. Sometimes, tubes just have a weak spot. Also consider that the tire could have been under inflated, which can cause the tire and tube to get hot, particularly after a long taxi. PA-38 tires in particular work a little harder, as they are small for the size of the plane compared to other types. Also check to be sure that you're running the correct ply rating tire.
My idea is to maintain a spare built up wheel to replace each on my planes quickly if needed. When I took my taildragger on a long trip, I left a whole tailwheel assembly built up and ready for shipping at home, so my daughter could ship it if I needed it. That tailwheel works really hard, with an operating pressure of 70 PSI, and if flown with too low a pressure, a shimmy can develop, which in the past has broken a steering arm - so I have extra incentive to keep that wheel round!