Models & Qualitative Behavior · Challenge problem

A sealed probe starts at $90^\circ$C in a chamber whose temperature is raised steadily, $M(t) = 20 + 2t$ degrees at time $t$ minutes. The probe obeys Newton's law $T' = -\dfrac14\left(T - M(t)\right)$. In the long run, the probe's temperature trails the chamber's by a constant amount. How many degrees is that?