Assuming you mean the equation $\kappa \frac{\partial^2u}{\partial x^2}=C_p\frac{\partial u}{\partial t}$, then they are all meaningful. In that case $u(x,t)$ is the temperature at point $x$ and timr $t$.

So $\frac{\partial u }{\partial t}$ represent the variation of temperature at a particular position and time, with respect to time. Thus, it represents a cooling or a heating, depending on its sign.