Another form of proxy temperature measurement
is called bore-hole temperatures.
What you do is you drill a hole in an ice sheet, or in a soil column.
And you measure the temperature as a function of depth.
What is happening with the temperature is that, in equilibrium,
if the temperature at the surface stays
constant for a very long time, the temperature will
increase with depth because of the generation of heat below the earth's surface.
This is called the geothermal temperature gradient.
The temperature goes up by about 30
degrees Centigrade per kilometer in the earth,
more or less.
If you have a sudden change in
the temperature at the surface, it takes awhile for
that news to difuse down into the ice core
or the rock column that you're measuring.
What would happen to the temperature inside is initially it
would only know about the warming right up at the surface.
And then as time passed the temperatures would relax toward
a new equilibrium where it's, again, along the geothermal gradient,
just going monatomically upward from the surface condition.
If you go out and you measure
the temperature today and you happen to see
something that looks like that, you can use what is known as an inverse method...
to try to back out how much the temperature changed, and when.
It's called an inverse method because, while reality goes from cause to effect,
the change in temperature at the surface
leads to this distribution of temperatures below.
The inverse problem has to
go the other direction, and go from the effect, which is this snapshot
of temperatures in the bore holes down inside the ice ice sheet,
and back out what the cause was.
How much the the temperature changed and when.
In general, borehole temperatures give you a much
smoother estimate of how the temperatures change with time.
Because if there's fast
temperature changes here, you'll never see that down in the interior.
Basically what you see is the same longer time-scale
overall patterns (of temperature change).