Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S25 / 3 / 2 / b / Solution

At late times $C\to 1/2$ and thermal equilibration requires $b_{0}C-b_{1}T=0$. Hence $\boxed{T(\infty )=b_0/(2b_1)}$. Both $t\gg k^{-1}$ and $t\gg b_1^{-1}$ ensure that the exchange and thermal transients have decayed.