Heat Current (Thermal Conduction)

There are a number of historical reasons for this, but the reasons the notation has remained is an important mathematical. Writing $frac{dQ}{dt}$ would imply that there was a state function $Q$, of which that expression was the time derivative. However, such a $Q$ does not exist. Another way to describe this is that the infinitesimal heat transfer $dQ$ is "not an exact differential." Similar, the infinitesimal work done by a system, $d$ is also not an exact differential; only by taking the sum do we obtain an exact differential $dE$, where the internal energy $E$ is a true state function.

Since $Q$ and $W$ are not state functions, it is often useful use notation, like $frac{Delta Q}{Delta t}$ that emphasizes that this ratio is not the derivative of a function. Another notation that is sometimes used instead of $dQ$ is $not dQ$, for the same reason.