Pressure increases boiling point not decreases it. Maybe I misinterpreted your comment, but that seems to fit the context of your comments as well. Pressure can be controlled by using a control valve to prevent vaporization. This is a common practice in industry and probably in spacecraft as well. On the other hand, if a pump must provide suction to lift the liquid it can cause boiling. This is a common problem with pumping solutions near the boiling point. I'm not sure how geothermal power stations work, but would guess they are naturally supplied by the pressure at depth rather than by pumps. I'm also not sure how a pressure control valve would work in conjuction with a turbine either. You raise some interesting issues that peaks my interest in learning more about geothermal power.

Michael Carr states in the "Encyclopedia of the Solar System" that the heat flow on Mars is estimated to be 40 mW/m2 compared to 75 mW/m2 for Earth. This is what you'd expect if the difference was due solely to the increased surface to volume ratio on Mars so I'm not sure how well accepted you geological variable estimates are. It's been 20 years since I worked on the heat or mass (usually similar) transfer equations for a sphere and don't have the time to rederive them right now so I don't know how that translates into a depth gradient but would guess it would be proportianally between a linear ratio of the heat flows and a square of that ratio. In other words a temperature gradient 1/2 to 1/4 that on Earth.

Freezing in the pipline is a big issue but one that I think technology can handle. It just requires appropriate insulation.

Regards,
Mark