Let's review a little thermodynamics - all heat engines require a heat sink in which to discard entropy. If they do not discard entropy, the system runs for a bit and subsequently fails to function. This means a couple of things - for your geothermal power solution to work, you need to reject heat somewhere, probably the atmosphere far above the colony, or maybe the ocean. Assuming you got that to work, you could then overcome the next thing that's going to kill you, and that's temperature.
Even with the wildest shielding, that shielding will eventually come up to the temperature of its surroundings, and your colony will get uninhabitable very quickly. The entire colony is going to have to be carefully air conditioned to prevent lethal temperatures, and the shielding should probably be liquid cooled. All of the heat absorbed by the shielding and the A/C system will have to be rejected back to your heat sink.
Handling the wild pressures at depth is the next thing we need to fix. If we are deep down and still have an open air connection to the atmosphere, it will kill everyone; periodically, we'll need to have air locks between levels so that pressures can be independently controlled. This is another problem though - if we don't have a connection outside, we don't have a way to ventilate. We'll need to generate oxygen and scrub toxins and CO2 from the air. There is no better way to generate oxygen than hydrolysis of water, but we'll need to get rid of the hydrogen produced - if we try to use it in any way, we just lose the oxygen we made, which we needed. So we use compressors to pump excess, unwanted hydrogen to the surface. Scrubbing the atmosphere takes, well, a scrubber - this machine uses a heater and a catalyst bed to absorb toxic substances.
For this to work for any length of time, the colony must be able to sustain itself - food, water and scrubber catalyst will be needed for continued operation. Water reprocessing is a must - your air conditioners will also be feeding into collection facilities. Crops will have to be grown under UV lamps in imported dirt. And to make your own scrubber catalysts means you'll need to be able to manufacture advanced materials underground.
On the whole, this is not actually possible with modern day tech. Our deepest mines right now extend some 4 kilometers below the surface, but have extensive surface support. The entire colony would have to be built in some kind of "goldilocks" zone where it conveniently didn't take on massive amounts of toxic subsurface gases by the hour, and had a freely available, easy to access heat sink, without having to worry about said heat sink breaking through the roof over your head and drowning everyone.
