Solving PDE w/ boundary having a partial time derivative term

Hello everyone,

I am currently trying to solve a heat transfer PDE that involves a boundary condition having a partial time derivative term. The PDE model is shown in the attachment, and the right boundary condition is the one that I am having trouble with. The PDE solver by default does not seem to be able to take such time derivative term into the calculation. Could anyone give me any suggestions what I should do? Thank you!

Best, Vince