@SJuan76 's answer is incomplete. He did the math to show the small cooling effect of, but didn't show the heating effect. I shamelessly copied his cooling numbers, and added heating numbers to compare.
Comets have a small cooling effect
Halley's mass is $2.2\times10^{15} \text{kg}$.
A cubic kilometer of water has a mass of $1\times10^{12} \text{kg}$
Oceans hold $1.35\times10^{9}$cubic kilometers, which gives us $1.35\times10^{21} \text{kg}$ of water.
So, the mass of the Halley is half a millionth of the ocean. If it is 200 C colder than Earth oceans when dropped, it would cool the ocean only by 4/10,000 C.
Comets have a large heating effect
Comets have both kinetic energy and potential energy as they fall to earth. The Kinetic energy will be at least as much as the orbital energy of LEO. The Potential energy is equivalent to mass times gravity times height. However, since gravity is not constant coming from LEO, the gravity times height portion is actually an integral $$\int_{surface}^{orbit} g(h) dh,$$ where $g(h)$ is force of gravity as a function of height. This function is $$ \frac{GM}{r^2}$$ where $GM = 3.98\times10^{14} \frac{\text{m}^3}{\text{s}^2}$. The radius or height of LEO is $6.671\times10^{6} \text{m}$ and the surface of earth is $6.371\times10^{6} \text{m}$.
Given the mass of the comet as $2.2\times10^{15} \text{kg}$, the potential enery equation: $$2.2\times10^{15}\int_{6.371\times10^{6}}^{6.671\times10^{6}} \frac{3.98\times10^{14}}{h^2} dh.$$ I solve that to be $1.2\times10^{22} \text{J}$.
How much energy is that? Given a mass of the ocean of $1.4\times10^{21}$ kg and a specific heat of 3850 J/kg*C, the heating due to potential energy is 22/10,000, or more than five times the cooling effect.
So basically, just dropping a comet from dead stationary in orbit, without any kinetic energy, will release potential energy many times more than the anticipated cooling effect.
