Imagine a rod that is initially at temperature $T_1$ and then brought into an environment with a lower temperature $T_0 < T_1$. How quickly does the body cool down? When will it have reached the environment’s temperature? What is the temperature profile throughout the rod, as a function of time?
This is essentially a worked homework set: a complete, step-by-step solution of the diffusion (or heat) equation in one dimension.