What is the effect of radius in a planet's steady state temperature?

Let’s say there are two planets, without an atmosphere, sharing orbit and equal in every way except their size: planet 1 is 10x larger than planet 2.

Heat into the planet $Q_{in}$ from radiation is proportional to the cross sectional area, $pi r^2$. Heat out $Q_{out}$ is proportional to the surface area, $4 pi r^2$. This implies to me that the ratio $Q_{in}/Q_{out}$ should remain constant for both planets, both scaling with $r^2$, resulting in the same steady state temperature. I find this rather counterintuitive – I’d have thought having a larger surface area to mass ratio would lead to a lower steady state temperature (making planet 2 the cooler one). Am I missing something? It just feels wrong.