Say you put something that is insulated in constant 150˚F water for 45 minutes, the center part won't be 150˚F for sure. Maybe only 110˚F.
But if you leave the item for 10 hours, with constant 150˚F water, wouldn't the center part eventually reach something like 145˚F?
What about 150˚F (same temperature as water)?
That's transient heat transfer. You could solve the heat equation for conduction, and is somewhat complicated in one dimension, with the equation $$ \frac {\partial u}{\partial t} = \frac k{c_p \rho}\left( \frac {\partial ^2 u}{\partial x^2} \right)$$
where $u$ is temperature, $t$ is time, and $\frac k{c_p \rho}$ is the thermal diffusitivity. This is a parabolic partial differential equation. Generally you just solve it with computers, and that's if we know more about the problem.
The real three dimensional equation is even more complicated. If we wanted to consider thinking of the water as able to actually move temperature around (and not just be $150° F$ on the surface all the time) then we would need to also involve fluid dynamics.
What's also interesting, it will only ever get closer and closer to the final temperature of $150 °F$ without ever reaching it.
