The opposite option to the underground greenhouse is placing the greenhouse on the roof of the house or rather making it on the attic level and making the part of the roof over the greenhouse transparent.
Warm air rises up so whatever heating system to warm the house you have, good thermal insulation of the roof is very important. But it's also economical to somehow use the heat gathering at the top of the house. Making a greenhouse there would do exactly that - its floor would warm up from the warm air rising from below. Just like in the case of the underground greenhouse, you can insulate the transparent roof of the greenhouse by making it from a couple or a few sheets of plexiglass with air gaps between them. You'd probably lose some heat from the living spaces due to the heating of the greenhouse, but have some fresh vegetables in winter.
Another, maybe more economical way to use the heat atop the house is to harvest it from the chimney, as Shubhankar Kulkarni suggested in his comment. Especially the part of the chimney which is above the roof, cause that heat is totally wasted to the atmosphere. One could make a small greenhouse around the chimney where the roof inclination is not too steep and make a ladder or a floor to reach it. Alternatively, one could make a specialized, horizontal platform to support the greenhouse even on steep roofs.