How much energy does the Moon transfer to the Earth, does this affect the Earth's surface temperature?
According to a slightly old estimate, the total power input from the tides is approx 3.7 TW [1]. Of this about 3.2 TW is from the moon (the rest is from the sun). Most of it goes into moving the oceans around, and some of it into doing the same with the land - but both ultimately end up as heat.

The question of how much this power affects the temperature of the earth is beyond my expertise, but it's a small amount of power at a planetary scale. Some very approximate comparisons:


Tidal power from the moon: 3.2 TW [1] 
Total global electricity consumption: 3-4 TW
Geothermal heat flow from the earth's interior: 30 TW [1]
Total sunlight hitting Earth (outside the atmosphere): ~175,000 TW [1,2]


[1] Munk &amp; Wunsch 1998; http://www.sciencedirect.com/science/article/pii/S0967063798000703 - probably paywalled.

[2] https://www.e-education.psu.edu/earth103/node/1004