Alex Blackwell on the Uplink.space.com board posted a link to some freely available journal articles on Mars:

Planetary and Space Science Volume 52, Issues 1-3, Pages 1-257,
Special issue: "Exploring Mars Surface and its Earth Analogues."
http://makeashorterlink.com/?C11835017

One of the articles calculates how deeply above freezing temperatures might penetrate the martian soil. This is important since it relates to whether the melting point might be reached if ice for example is several centimeters subsurface:

Theoretical prediction of the thermal conductivity and temperature variation inside mars soil analogues.
F. Gori, and S. Corasaniti
Planetary and Space Science
Volume 52, Issues 1-3 , January-March 2004, Pages 91-99

Two graphs in this paper gives the depth to temperature variations for both dry soil and frozen soil.

Graph for dry soil.

Graph for ice filled soil.

The graph for frozen soil shows above freezing temperatures can be reached more than 20cm, 8", subsurface, starting with a temperature of 298K at the surface.

Actually the melting point should be reached at even lower depths than this because the minimum temperature the authors use is 148K. Apparently they take this from the minimum Summer temperature anywhere on Mars.
However, an LPI report models the surface temperature range at the Pathfinder site, which is near the equator, and gives the range as about 190K to 290K, for a variation of 100K:

The Martian Surface Boundary Layer.
Authors: Wilson, G. R.; Joshi, M.
Journal: 31st Annual Lunar and Planetary Science Conference, March 13-17,
2000, Houston, Texas, abstract no. 1678
http://www.lpi.usra.edu/meetings/lpsc2000/pdf/1678.pdf

This would be a more realistic temperature range for a near equatorial site and would result in the melting point being reached at an even lower depth than modeled by Gori and Corasaniti.

Modeled Pathfinder temperatures from "The Martian Surface Boundary Layer".

Bob Clark