How do we know the temperature on the planets? I was watching a show and they were saying that the temperature of Pluto (I know it is not a planet) is about $-300 {}^\circ F$.  I know that depends where in the orbit Pluto is, but how do we determine the temperature?
 A: There's a few ways the temperature can be measured remotely.
The easiest way is to measure the amount, and for bonus, spectrum, of the radiated heat. All objects greater than Absolute Zero radiate a certain amount of energy. The wavelength spectrum can be determined by Planck's Law, and the amount of energy by 
the Stefan-Boltzmann law, both of which are listed below.
$I'(\lambda,T) =\frac{2 hc^2}{\lambda^5}\frac{1}{ e^{\frac{hc}{\lambda kT}}-1}$
$j^{\star} = \sigma T^{4}$
So, to determine the temperature, all one needs to do is measure the energy over the waveband of interest, and one can get the temperature.
In the case of Pluto, an easier method can be done. We know the total amount of energy going toward Pluto, based off of its distance from the Sun. We can use this to measure the average temperature of an object receiving that amount of energy.
The last method involves knowing the physical properties of the object. For instance, Pluto has a atmosphere of Nitrogen, Carbon Dioxide, and Methane. The atmosphere will freeze as Pluto moves further out in its orbit. The temperature can be inferred by what materials haven't frozen out of the atmosphere yet, which can be determined with spectroscopy.
Typically, the first one is done, and the second when a more accurate method cannot be used (IE, no direct spectrum of the planet observed).
