How does this happen? Why would something which reflects light on the outside get hotter than one which absorbs light? This makes no intuitive sense to me.
Remove convection/conduction as heat transfer methods, and you end up with two numbers dictating radiative balance:
Percent reflectivity in the bands it's exposed to
Percent emissivity in the bands it's emitting
The balance between these dictates temperature, and they're generally inversely correlated. Mirrors are good reflectors, but very poor emitters.