I'm tempted to state simply that all the Mars models you're familiar with are wrong, but that would be unhelpful. Let me explain WHY they're wrong...

Subsurface temperature is determined by 3 factors:-

1) surface temperature Ts
2) heat flow Q
3) thermal conductivity K

T(z) =Ts+Q/K

That's all nice and simple. Now let's compare Earth and Mars and supply a useful yardstick: In a sedimentary basin on Earth, thermal gradients are around 30-35 K/km (Yardstick check - The gold mines in South Africa are several km deep and the rock is warm enough to steam if you pour water on it)

1) On Earth, surface temperature is around +15 C on average (we're talking year-round global average here. ) On Mars it's -60 C

2) *IF* Earth and Mars are made of the same stuff, then Mars has 1/10 the mass and 1/4 the surface area so Q should be about 40% of Earth's. In fact, Mars' mean density of 3.9 vs Earth's of 5.5 shows that it is made of different stuff. (this is a little recognised point. It isn't crucial to the result, but it shows that most people who talk about heat flow on Mars don't know what they're talking about)

There is a clear compositional gradient through the solar system from Mercury (huge metallic core) through Earth and Venus (biggish cores) to Mars (small core) and then the gas giants (volatile-rich). Mars has fewer metals, more non-metals and oxides, perhaps more "volatiles" than Earth. (BTW, Gold is relatively volatile. Due to the zoning of the solar nebula, Mars probably has 4 times as much gold as Earth. If only it had plate tectonics and granites to concentrate the incompatible elements!)

If you look at the main radioactive elements, U and Th are early-condensing metals and would be less common on Mars than Earth whilst K is a later condensing substance (it depends in part on the chemical species that condense as well as the element itself, but you see what I mean). So, weight-for-weight Mars has about 70% of the radiogenic heat production as does the Earth.

70% x 40% = 28%

3) Most rocks are pretty good insulators. Liquid water in the pore space helps a bit but this doesn't add much conductivity unless you have a huge geothermal system convecting actively (usually with transport in the vapour phase - steam) Interestingly, ice is quite a good thermal conductor - much better than rock or liquid water. So if your rock is cold enough to have permafrost, it increases K and depresses thermal gradients.

===============================================

Collectively, these effects conspire to give thermal gradients on Mars that are certainly less than 10 K/km and may approach 5 K/km

If we start at -60C at the surface, we have to go down SIX to TWELVE km to reach the melting point of pure water. This doesn't leave much, if anything, between the Permafrost and the bedrock.

At the equator, mean annual temperatures are about 10-15 K warmer, so you "ONLY" have to drill 5-9 km. At the poles, the annual temperature is a frightening -125 C. You'll need to go down 12-25 km to find pure water!

===============================================

As a sanity check, consider Antarctica. The mean annual surface temperature there is rather comparable to Mars. There's a lot of ice, so the thermal conductivity issue is covered, and there's only a difference in Q.

How thick is the Antarctic ice? - three to five km. Doesn't this match nicely, allowing for a ratio of 2-3 in Q???

This is why the Clifford/Fanale school of thought on shallow aquifers is preposterously wrong, and why it's so important to look for other materials than pure water.

I went out on a limb with liquid CO2 and although that isn't dead, it has taken a bit of a licking from sulphuric acid. The optimum eutectic in the H2SO4-H2O system is liquid down to -74 C, so it could flow on the surface of modern (non-polar) Mars.

Trouble is, if acid that concentrated hits rock, it reacts. The result is sulphatised rock (e.g. Meridiani), and dilute sulphuric acid. As the acid weakens, it freezes.

That's why the last place you want to put your mobile acidic solution is under the ground - it has too much opportunity to react with rock and dust and lose its potency. You need to insulate the acid from the rock with water ice - a non-reactive mineral on Mars!

How do you generate the acids? One method is from sulphate-rich volcanic dust, ash and exhalative deposits, interbedded with snow and ice. The sulphate can potentially form sulphuric acid, melting some of the ice. The acid will trickle along the layers in the ice and emerge at the edge of the snowpack where it can react with rock.

So the environment that we should be imagining for Meridiani is not the shore of some mythical acid ocean, but actually the edge of a retreating glacier or icecap funnelling acids down to the plains below. The edge of the ice would weep acid onto the adjacent rocks, gradually transforming a huge area into sulphate deposits...