Could our bacteria survive subsurface there?
Some of them may be able to, if there is liquid water and some chemical disequilibrium, some source of chemical energy.
Modern geothermal gradients on Mars and implications for subsurface liquids. - 2001
Geothermal gradients; Earth: typically 30 - 35 K/km, though
Geothermal gradient cites 25 - 30 K/km. "The effects of weather, the Sun, and season only reach a depth of roughly 10–20 m (33–66 ft)."
The deepest mines are some South African gold mines near Johannesburg:
Mponeng Gold Mine (4 km, 66 C) and
TauTona Mine (3.9 km, 55 C) and
East Rand Mine (3.585 km, 50 - 60 C) --
Johannesburg has a mean temperature of 15.5 C -- giving a gradient of around 10 K/km there.
The
Kola Superdeep Borehole has a depth of 12,262 meters with a temperature more than 180 C (
7 facts about the Kola Superdeep Borehole). Nearby
Murmansk has a mean temperature of 1.1 C. That gives a gradient of 15 K/km.
The
German Continental Deep Drilling Programme (KTB) has a depth of 9,101 meters with a temperature of more than 260 C. Nearby
Munich has a mean temperature of 10.1 C. That gives a gradient of 27 K/km.
KTB's gradient was unexpectedly high compared to Kola and those South African gold mines. But Kola and the gold mines are on "cratons", blocks of old continental crust.
Back to that Mars paper.
Its authors estimate gradients of 10.6 K/km for dry parts and 6.4 K/km for icy parts.
They use concentrated brine as a reference, with a melting point of - 25 C. The best case is Mars's equator, with an average temperature of around 230 K or -43 C.
Estimated depths (brine, dry): 1.7 km, (brine, icy): 2.8 km, (water, dry) 4.1 km, (water, icy) 6.7 km.
So it's a long way down to whatever organisms might still be living on that planet.