The only reason the equator is warmer is because the sun is closer to that area in it's path. Thus more heat is reflected there. Areas where an equal amount of heat is dissipated from the surface but very little is reflected back would, of course, be colder. But do not be confused, even the colder areas have a lot of heat.
If it weren't for the sun, the entire Earth would be like the arctic 24/7, correct? Since the equator is only warmer because of the sun.
So if you put a big mirror above an arctic world, it will shine back enough heat to cook an egg?
By that logic, the mirror in my bathroom should have instantly scorched a hole through the wall.
I don't think you understand how mirrors work. They reflect, they don't draw-in heat from an entire planet like some sort of magical vortex, shooting it back at 1,000 times the strength of the entire combined heat, while converting much into light.
Put a mirror in an oven and see how bright it gets. (and if it melts through the door, shooting a beam into space)