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In kim stanley robinson's mars trilogy One of the terraforming techniques that they use is a giant lens that carves (using heat) out a massive cannal between the Northern basin end the hellas basin. Something I always found a bid sketchy nut for fun I've compared the numbres with something from zubrins works:
Zubrin says that by building a 125 km mirror with a mass of 200 000 tons could provide a 5°kelvin temprature rise for anything below 70° this is 20/180's (11%) of the martian surface a total area of 1,59E13m² (greater then the European continent)
But if you can double the temprature by halfening the surface area (a 10° rise for 7.96E12m²) you can actually get a 1280° rise by lowering your focus point to 6.22E10m² (the size of lake huron) or 40 960°K by 1.9E9m² If the reasoning fits then carving a canal wouldn't be all that impossible.
You can't double the temperature by halving the area, you must decrease the area by a factor of 2^4, or sixteen, all according to the Stefan–Boltzmann law radiance (w/m^2) is 5.67*10^-8 * T^4
Also, Zubrin likely means a cumulative effect of using the mirror to heat the poles in order to release CO2, thereby heating the rest of Mars by the greenhouse effect. A 125km mirror would have little effect on its own, as it would only add about 0.034% more solar heat.
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