I would concentrate on the by pass valve and it's plumbing.
If it is an after market 3 valve system I would assume the center valve is not in the off position. Does it run hot for more than a few seconds a any faucet? If it is a short duration effect and the center valve is open that may just be migration through that valve.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles