I don't think dumping heat into the ground would work for any meaningful amount of time - both on Earth and on Mars the dirt and rock are not a very good conductor of heat, so you would quickly heat up your local "heat island" in the ground soon loose the temperature difference to run our heat engine on. Might work for pulsed operation where you wait for the affected area to cool down, but I am skeptical, given that a similar system is used for heat storage on Earth and it can take months to years for the temperature to return to natural values.

Most likely you would have to use air cooling, with lots of fans to push the thin atmosphere through massive heat exchangers. The overall lower atmosphere and general ground temperature (due to Mars being less heated by the Sun) should help offset this somewhat compared to cooling a reactor of the same power output in the vacuum of space.