Initial values AND solution as initial condition

Hi,

I've got (maybe) a very simple question, but I can't find any answer to my problem.

I'm solving a two-step heat transfer problem, the first one is stationary in order to get the temperature distribution on the domain A.

The second one is transient, in which I would like to add another domain, B.
The problem is : I would like to consider a specific initial value for B (T_init=f(y)) depending on the y-axis, AND use the solution of the first study to re-use the final temperature distribution in A as initial condition.

It does not seem possible. It is possible to make either one or the other. Has anyone a tip?

Thank you very much