Recently during a discussion with a colleague we got into an argument. The discussion involved imagining a heated solid body at some temperature $T$ which is immersed in a large fluid medium maintained at a temperature $t$. After a long enough time has passed the solid will ultimately come in thermal equilibrium with the surrounding fluid medium and attain the fluid temperature $t$.
My colleague argues that after the time when thermal equilibrium is reached the boundary of the solid body can be treated as insulated/adiabatic as there will be no heat transfer between the solid and the fluid.
Is his conclusion correct ?
Answers with mathematical explanation supporting or refuting the claim are a bonus.