QUESTION:
How do they know how hot things are on the stars or planets?
Why are the colors indicators of heat?

ANSWER from Sean W. J. Colgan, KAO Astronomer, November 13, 1995:
I've reversed the order of the questions, for clarity:

From observing the world around them, scientists have found that the cooler
an object is, the redder is the light it emits. For example, a stove burner
is red, while molten steel, which is hotter, is white. Flames are red on
the outside, yellow in the middle and blue on the inside, where they are
hottest. Most everyday day objects are so cool that the light they radiate
because of their temperature is at wavelengths so long that our eyes can't
see them. These colors are called infrared and it takes special equipment
to see them. Night vision goggles often can see infrared light. Everyday
objects appear the color they are not because of the light they radiate,
but rather because they reflect light from other sources. A red car, for
example, reflects red light from the sun or a street light just like a
mirror. The paint on the car absorbs all the other colors, like yellow,
green and blue, so all we see is the red.

When astronomers look at the sky, they find that stars are different
colors, too. It is difficult, but not impossible, to see this with the
unaided eye - some stars appear red while others appear white. With a
telescope, the difference is obvious. From careful measurements of the
colors, astronomers can estimate the temperatures of the stars. The same
idea applies to the planets, except we must look in the infrared. Planets,
like cars, are not nearly as hot as stars and so emit light only in the
infrared. The colors the planets appear to our eyes are again from
reflected sunlight and not the temperature of the planet. Saturn appears
yellow because of chemicals in its atmosphere. Mars appears red because of
the rocks on its surface. If we look
at infrared light, however, we can easily measure the temperature of each
planet.