I would not adjust a heater unless the tank temp drops very low at night. You light will drive the temp up if the temp is already higher before the light turns on. Is your hood vented? A wooden canopy/hood can hold heat from the heat sink well if not vented well.
I doubt that the bleaching of your birdsnest or monti cap is heat related, though. 81 degrees F is not high enough to cause bleaching unless your water condition is less than desirable. Most SPS's need a well-established tank with stable parameters. I got a feeling that it's more of a tank maturity issue. Even when you use old rocks, sand, and water, your SPS's will sulk for awhile when you move them into a new tank. Their colors will dull for sure.
A number of my A. millipora and other light loving SPS's including pink birds nest were colored up beautifully at only 8 inches from my 250W MH bulbs in my 120 where temp fluctuated more than 78 to 83 range that my 180 is holding. I am afraid that you have to take it a bit more slowly. Be patient.
I remember having a heck of a time keeping a pink birds nest in my 29 gallon tank which was only six months old while Bali green slimer and other tougher SPS's such as monti cap and digi were all fine. It became possible to keep more delicate SPS's as my tank matured.