"depends exactly WHERE you drill, but in general the poles are colder so you gotta drill deeper."

It doesn't seem to me that surface temperature should have a significant affect when dealing with rock depth more than a couple hundred meters:
Geothermal Gradient [regarding Earth]:
"Temperatures at the surface of the earth are controlled by the Sun and the atmosphere, except for areas such as hot springs and lava flows. From shallow depths to about 200 ft (61 m) below the surface, the temperature is constant at about 55°F (11°C). In a zone between the near surface and about 400 ft (122 m), the gradient is variable because it is affected by atmospheric changes and circulating ground water. Below that zone, temperature almost always increases with depth. However, the rate of increase with depth (geothermal gradient) varies considerably with both tectonic setting and the thermal properties of the rock."
http://www.enotes.com/earth-science/geothermal-gradient

It seems to me that at depth of +200 meters on Mars, the temperature will vary mostly due to the thermal properties of the rock rather than surface average temperature. And when one goes deeper, say 1 km in depth, the surface temperature would have even less affect.

Related to this:
"Permafrost and gas hydrates are commonly found together; however, there is no direct causal link between them. In cold polar regions, two parallel events occur: 1) with surface temperatures hovering around -12°F, even with a normal geothermal gradient, sub-freezing temperatures can persist to depths of 600 meters or more, and 2) the very low temperatures, when combined with steadily increasing subsurface pressures, allow methane hydrate to be stable at depths ranging from 300 meters to 1 kilometer.
...
Geological parameters that affect gas hydrate formation include subsurface temperature, pore pressure, gas chemistry, and pore-water salinity. The geothermal gradient in Arctic regions with hydrate accumulations ranges from 1.0°C to 8.0°C/100 meters."
All About Hydrates Arctic Regions

Mars temperature:
"While the average temperature on Mars is about 218 K (-55 C, -67 F), Martian surface temperatures range widely from as little as 140 K (-133 C, -207 F) at the winter pole to almost 300 K (27 C, 80 F) on the day side during summer."
http://www.nineplanets.org/mars.html

So in terms of top layer of surface temps: 140 to 300K
But what is the variation in temperature if one were to merely go 1 meter in depth? It's not ever going to be a colder than 140 K but instead will be closer to the average polar temperature, so how much of difference is there between average polar temperature and average equator temperature?
Could the difference average temperature be a little as 30 C?