First let's look at the Earth.Most of our warmth on Earth is geothermal.It's essential for life as we know it.
Our nice thick atmosphere is maintained by a combination of biology and geothermal activity.
Since Mars shows no techtonic activity or vulcanism it's at a disadvantage right off.
It also has a very weak magnetic field.The core is very cool relative to Earth's.
Earth's geomagnetosphere has huge influence over the atmospheric density.
Down here we are protected from solar winds that can strip atmospheric gasses by shearing them away from the planet..Like water running on a bar of soap,it will eventualy melt away.
To terraform mars would be a daunting task.
It has been suggested that we could thicken mars atmosphere by melting the polar ice which is largely water and carbon dioxide ice(dry ice).
That would not be enough to get it to earth density but it would help.
After that we could plant microbials that produce more co2 that retain solar heating.
But that's not enough since mars' low gravity also needs to be considered.
Some believe we could "heat up" mars' core with nukes dropped into the core but that would be a huge task.
I believe dropping comets on mars would work better.With comets we would add atmosheric gasses and water and melt the poles at the same time by impacting the comets at the poles.
The problem of no protective magnetic field would still remain.
If humanity does ever get a foothold on mars I would think it would build colony domes covered with native soils. That would provide insulation from solar radiation and small meteoric debris that commonly falls on the planet.
I believe going to mars is itself a loosing prospect.
It would be far easier to harvest the asteroids for materials to construct space habitats. Everything we need is out there floating in microgravity ready to be scooped up and refined.
It's estimated that a single hab cylinder a killometer in diameter three killometers long could support several hundred thousand people in a self contained system.
And space is a great place to harvest solar energy.
If humanity needs a place to move to in the future,that would be the best way to do it.And with spaceborn habitats we could move them out away from the expanding sun as it nears it's end of life.
Mars is a great fantasy but it's much harder to deal with gravity than not.
Space habs are the way to go.Mars realy offers little we can't get in the asteroid belt.