Simplified down:

heat / time = q/t = heat flow

temperature increase / time = :delta: t / t = heating rate

heat flow / heating rate = (q/t) / ( :delta: t / t) = q / :delta: t

Well, q / :delta: t = Cp = heat capacity of whatever you are looking at.

Well, the heat capacity is a constant for whatever you are looking at (ok, it is not, it changes with temperature and pressure, but whatever, like I said, simplification).

Well, if your :delta: t is big, then you q has to be "big" as well in order to make it equal Cp. If you can make your :delta: t smaller, you need less heat to satisfy the equation; ultimately meaning you can use a smaller sample.