It may be different there than here, but in the states, the challenge in getting at that lower level coolness (it's about 50-55F here) or heat in the winter is getting it without mold and condensation problems. There was an old tradesman on another US forum who described something to me (i didn't completely follow it) as being a pass through of air underground and back up, and he said it worked well. he lives in either VA or TN in the US (both are very hot).An excellent source of coolth is the ground beneath us. A couple of feet below the surface here, the temperature is 8'ish to 11'ish C all year round.
Besides stopping heat getting inside the building envelope to start with, and minimising the amount of energy required to cool the air within that envelope (with insulation and thermal mass and sun shielding (could be as simple as a verandah) - details like people use in the design of their buildings in really hot countries) e.g.
I think moving air through the ground before bringing it into the house would be better than air conditioning - like this, perhaps:
Optimization of operating parameters of earth air tunnel heat exchanger for space cooling: Taguchi method approach - Geothermal EnergyIn the present study, CFD-based parametric analysis is carried out to optimise the parameters affecting the temperature drop and heat transfer rate achieved from earth air tunnel heat exchanger (EATHE) system. ANSYS FLUENT 15.0 is used for CFD analysis, and k-ε model and energy equation were...geothermal-energy-journal.springeropen.com
Of course, the OP doesn't have the luxury of re-designing/re-building their house! Cross-ventilation (both from side-to-side - during the day - and top-to-bottom - at night) and sleeping downstairs are two quick, easy and cost-free solutions.
Don't forget the cooling effects of plants and water too.
Challenge 2 is that if too much load is put on a segment or mass of earth underground, it will just come closer to the temp of the air being passed through it.
I know nothing about geothermal but expect that what happens is the well is drilled, something that will allow the ground adjacent to the well to absorb heat is installed and the piping runs through that (and whatever they require for mass is probably a good starting point for an estimate).
Or you can go all out as some have done where I grew up and build a house that's actually underground except for the top foot or so. There was one where I grew up - not sort of part of the way underground or built into a hillside, but with all floors underground. The owner said that was a cheaper way to build and own per square foot.