It's also quite obvious that you would have access to the equations, numerical values and quantitative comparisons that are need to defend one theory against another.
TV science programs usually ignore/bypass such arcane material
for reasons of brevity and to secure the interest of the layperson,
who would otherwise be bored to tears.

So when you indicate that a huge [hypothetical] moon orbiting
Mars aeons ago wouldn't generate enough tidal heat-energy in the martian crust to make a benign surface environment...Well...pardon the pun, your argument stands on pretty solid ground in that case....considering you would have easy access to such geophysical values, etc...

But!...It makes me wonder...could there have been an close analogy to the present-day climate in Iceland in a locarge but localized area on Mars billions of years ago?

As You know, Iceland would have a climate and ground conditions comparable to northern Greenland, or even Antarctica, were it not for two things:
(1) The Gulf Stream.

(2) Tremendous and widespread geothermal activity not far below
Iceland's surface.