Well, maybe. How?
It's the cold side of the engine. The top of the engine in contact with the working fluid is 64 or 65°F
The power cylinder is an "island" near the middle, within this cool zone above the displacer and appears to be about 10° warmer.
Within the power cylinder is a piston moving up and down generating friction, driven by the expansion (work) of the working fluid.
The pretty obvious source of heat centered on the power piston is friction. If anything the heat generated by friction is migrating back into the cooler working fluid not coming out of it and somehow gathering around the power piston.
Heat moves, generally speaking, from hot to cold not the other way around. The power cylinder is hot surrounded by the cooler zone above the displacer.
There is some localized compression of gas in the cylinder I suppose, but that would also be the result of mechanical "work". Not likely a factor IMO.
The heat of friction and/or compression comes from the WORK done by the working fluid, sure.
I assume however you are talking about direct heat transfer from the presumably cool gas to the heat laden cylinder.
You seem to think heat can spontaneously gather in one spot, moving from cold to hot.