A homogeneous, insulated object with a non-uniform initial temperature will eventually reach thermal equilibrium. Which point in the object takes the longest to reach this equilibrium? Intuition tells us that points “in the middle” of the material will generically reach this equilibrium temperature faster, and points “far from the middle” (i.e. at the boundary) should take more time to reach this temperature. The hot spots conjecture is a formalization of this intuition.