The inside of the hive gets no sunlight. Therefore can not reflect or absorb sunlight. It is the color of the outside of the hive, not the inside.
I like white. I like free paint also. We don't have that much of a winter compared with up there. Cold at night. Also dark at night. I am married to a high school science teacher and would as her about all the science of painted hives, but she has fallen asleep on the couch and being 7 months pregnant (crazy and unpredictable), I aint waking her up to ask.
Aw come on, Allen...wake her up and ask her!!! You ain't scared of a 7-month pregnant wife are you? (Said safely 200+ miles away from you.