"It seems likely to me that Mars should have a different gradient than Earth. But like Earth, Mars should have areas with different gradients which would depend upon numerous factors, but one them being the "thermal properties of the rock"."

Nick has said:
"Introduction: Historically, Mars has been viewed
as an Earth-like planet and the consensus for geother-
mal gradients has been close to that for Earth or no less
than 50% of that value [1]. As a consequence, liquid
water is envisaged as a likely occurrence in the rela-
tively shallow subsurface (1-2km). Recent data from
MGS, however, has added weight to the alternative
view [2] that Mars is in fact much less thermally active
than the Earth and has significantly lower heat flux and
geothermal gradients (1/4 to 1/3 that for Earth). Conse-
quently, liquid water requires exceptional local condi-
tions before it will be found in the upper few km of the
regolith and the most likely liquid in the subsurface
may be liquid CO"
Modern geothermal gradients on Mars

If we assume the heat gradient is 1/4 of Earth or even 1/10th, what heat gradients of Earth do we include?
Do we use some average heat gradient number or should include any value from 500 K per km to below 20 K per km?

Nick says:
"Geothermal Gradients: For a given heat flux, geo-
thermal gradients depend on thermal conductivity. On
Earth, typical geotherms are around 30-35 K/km. Eve-
rything on Earth is water saturated, and water is actu-
ally a relatively poor conductor of heat (although in
convecting systems it is an excellent advector). In the
upper layers, at least, of Mars we expect water to be
frozen. Ice is a much better conductor of heat, espe-
cially at lower temperatures, so for ice-filled porosity
on Mars we expect conductivity 25% better than on
Earth. For dry but compacted regolith, we expect con-
ductivities 25% worse than on Earth. Consequently in
dry regions of Mars we might find geothermal gradi-
ents of 10.6 K/km, while in ice-saturated zones we
would expect values of a mere 6.4 K/km."

So, in ice saturated zones, Nick comes up with 6.4 K per km.
But in the reference I gave earlier regarding Earth arctic:
"The geothermal gradient in Arctic regions with hydrate accumulations ranges from 1.0°C to 8.0°C/100 meters."

Or 10 K to 80K per km. If we 1/4 these values: 2.5 to 20K per km. Or even if we 1/10th them: 1 K to 8 K per km- Or an "average" of 4.5 K per km.