The issue comes from the intial temperature setting. "Internal temperature" is not defined for all the nodes in the Thermal Loads boundary conditions, but only for the exposed faces nodes. In that study, the internal nodes temperatures go from a "0K" (unknown) to a heated temperature of ~90K...
a) in the transient study, select the thermal load initial temperature for the Solid Body, instead of the 3 exposed faces (only).
b) set a first steady-state thermal analysis with a convection (whatever value), and a temperature of 300°C.
That model thermal result at steady state will have the 300°C initial temperature for all nodes.
Then set a 2nd study, as thermal transient, with the initial temperatures from the steady-state (1st) thermal study.
I have run the studies in these ways, and both solutions work fine, in line with the analytical results.
Thank you! That worked perfectly, it makes plenty of sense actually.