It's really just heat loss by conduction in a cylinder with a height determined by the rate of hot magma added to the system (really, you can say the magma is added in in meters/time or cubic meters/time ... it's done in 2D but axially symmetric).
And your right - once I really thought about...
It's not homework :) It's the initially confusing results of a numerical analysis I'm doing on the thermal evolution of magma sill stacks ... but I think I've satisfied myself that this is a product of reduced surface area for the smaller sill stack (my spheroidal picture is kind of distracting...
Imagine magma flowing into two chambers in the Earth from some deep source. It's hot (1500 K).
For one source (SOURCE 1), the flow of magma into the chamber is 10 m/s
For the other (SOURCE 2), it flows in at 5 m/s
After 5000 years, we measure how much of the magma is still above 1150 K...
