How exactly are you going to build a radiator going from the Earth to the Moon?
Please keep in mind that:
1. A Space Elevator would be considerably shorter than the distance from Earth to Moon. Regardless, there is no known material strong enough to support its own weight, let alone a payload, to geostationary orbital heights. [1]
2. The Earth and Moon are not tidally locked. You'll need a slip-path around the Earth's equator (or a gimbal at a pole) to allow the Earth to spin underneath the radiator pipe. Which (at the equator) will be moving at roughly 1,000 mph (1,700 kph).
3. Heat doesn't flow from colder to hotter objects. You'll need a rather large heat pump to make this project work.
4. If you're planning on radiating Earth's heat to the Moon, well, I suppose you could create a large lasing facility. There's been some theoretical work done in this area which you might find ... illuminating.[2]
But keep in mind: there's no need to direct those beams at the Moon. Space itself is a sink, and will absorb any and all energy beamed to it. What's critical is to balance the Earth's energy budget, which is presently too great by roughly 0.60± 0.17W/m².[3] Given Earth's surface area of about 510 million km², that works out to an excess energy of 306 TW. That compares against 12.3 TW total human world energy consumption.[4]
Whilst I'm not a fan of such geoengineering projects, the concept of a solar sunshade, or equivalent aerosol blocking, strikes me as more tractable.[5] It's easier to keep energy off a thing than to get energy out of a thing. Though what's being discussed here are shades of never-gonna-happen impossibility.