If the BDZ blows off the atmosphere then you could possibly bombard the planet with comets. It'll be like throwing ice cubes into a bowl of hot soup. The comets would melt and help cool the surface.
Would they, really? Or would they have kinetic energy in excess of what they'd need to melt (or vaporize) themselves, thus
raising the average temperature?
Gravitational potential energy is given by U = -GMm/r where G = 6.67384e-11, and using Earth as an example, M = 5.972e24 kg and r = 6.371e6 m. Gravitational potential energy is defined as zero at an infinite distance, and is (as you can see) negative at finite distances. The kinetic energy of a falling object will be equal in magnitude but opposite in sign to the change in its potential energy. Using the values above, we get a value of 6.26e7 J/kg for an object falling to the surface of the Earth, or 6.26e4 J/g.
So, how much energy does it take to melt the comet? Let's assume it starts out in thermal equilibrium with the cosmic microwave background radiation at about 3 K. We need to: 1) heat ice from 3K to 273.15K, 2) melt the ice, 3) heat water from 273.15K to 373.15K, and 4) boil the water. Let's assume a mass of one gram for simplicity's sake.
Ice has a specific heat of 2.03 J/gK, so 2.03 * (273.15 - 3) = 548.4 J.
Water's latent heat of fusion is 334 J/g, so that's another 334 J.
Water's specific heat is 4.179 J/gK, so 4.179 * 100 = 417.9 J
Water's latent heat of vaporization is 2260 J/g, adding another 2260 J.
This brings the total energy needed to boil a cosmically cold piece of water ice to 548.4 + 334 + 417 + 2260 = 3559.4 J/g. We have 62600 J/g available, about 59040 J/g more than we need to vaporize the comet. The specific heat of water vapor varies with its temperature, but it's about 1.85 J/gK. Naively assuming that all the energy goes into heating the steam, the final temperature of the comet would be over 32,000K.
Gently lowering comets onto a planet might cool it down, but bombarding it with them will NOT.
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