Let's look at Mars and see what we can guess (intelligently) about geothermal gradients and the behaviour of hot water, plus its frequency and vigour...

Geometry

Compared to the Earth, Mars has 1/10 the mass, and 1/4 the surface area (1/8 the volume - note lower density. This is important). Geothermal gradients on Mars are therefore expected to be 4/10 those on Earth, if internal composition is the same. (actually, the answer is damn close to the ratio of gravity - 38%, for geometrical resons).

However, the lower bulk density of Mars tells us that it has different composition to the Earth. There is a density gradient from Mercury - (Venus/Earth) - Mars. Mercury has a huge metallic core. Mars has almost none.

Radiogenic heating and the Solar Nebula

What are the chief radioactive elements that contribute to modern heat flow? Uranium, Thorium, and Potassium. These are not exactly equal in their contribution, and the ratios vary with time due to different half-lives, but as a first approximation, let's assume they are roughly equal, averaged over time.

Uranium and Thorium are refractory metals. They condense easily from the solar nebula and would be concentrated along with other metals. Later, once planets form, they do not chemically join with the core, but are "incompatible" elements that get concentrated in the crust. Nonetheless, metal-rich planets are rich in 2 of the 3 radiogenic elements.

Potassium is relatively volatile. It condenses with difficulty at a distance from the centre of the solar nebula. It is concentrated in those bodies that LACK a good metallic core. In subsequent planetary evolution it is moderately incompatible, and is concentrated in the crust and mantle.

So let's compare Mars and Earth. As a rough rule of thumb, there may be a factor of 2 or 4 enrichment/depletion between the two planets of elements that are close to the volatile/incompatible bopundary (Claude Allegre has done good work on this). As an interesting aside. Mars has got probably 4 times as much gold as Earth, oper unit mass, but without plate tectonics, hydrous minerals, and granites, it will not be concentrated into ores.

Back to reality - Mars will have less U, and less Th, but more K than earth. On balance, it will have less radionucleides, making its gothermal gradient 1/3 to 1/4 that of Earth.

Heatflow on Earth and Mars

Mars also shows evidence of stronger earlier differentiation than Earth (odd, but apparently true). We expect the radiogenic elements to be nearer to the surface and heat loss over time to have been more efficient than the Earth, despite its lack of plate tectonics (Contra-intuitive, but well-documented). This suggests a value around 1/4 that of Earth is a good estimate.

Earth has a heatflow of 15-40 K / Km, so Mars will have 4-10 K/Km.

Mean surface temperature on Mars is -60 C. So the melting point of pure water will be at 6-15 Km depth.

Hot Springs

If liquid water is produced from a hydrothermal system, it will flush brines out, so cannot be much colder than this. So geothermal springs on Mars must rise from depths of ~ 10 km.

Local hot spots may reduce this significantly, but we still see sources of water restricted to several km depth in the regolith of Mars.

Note that with depth, pressure increases, so water will tend to boil at depth, as in geysers on Earth, but at greater depths, especially given the low atmoispheric pressure above.

it is likely that boiling will occur at depth, not at the surface, and that steam columns will ascend from 2-4 km depth and vent at the surface.

As the steam ascends, it will cool, and freeze directly to ice (since there is so little room between the boiling and freezing oints on Mars). This will clog most of the pores, except for "chimneys" of steam, rising through a permafrost matrix.

At the surface, further cooling and expansion is likely to lead to ice towers, not hot springs...

Power and Mass

Geothermal power on Mars, if it exists (and note that even the youngest lava flows are ~ 1 million years old - On Earth, those volcanoes would be declared extinct!), would be driven from great depth, and only a wisp of steam would finally emerge at the surface, IMHO...

Geothermal power is rarely economic on Earth, and only in areas where plate-boundary volcanism, "hot" granites, or thick sedimentary basins exist. SInce none of these are likely on Mars and the average geotherm is ~ 1/4 that on Earth, it is unlikely that we can afford to transport to Mars a drilling rig powerful enough to tap geothermal power. (It would be far easier to ship a few tens of tons of a nuclear power plant, than a few thousand tons of drilling rig)

Of course, if there ARE hot springs, then we're laughing, but they must be invisible to IR, since we haven't seen them yet despite a planet-wide 100m pixel IR survey.