The following is a rule of thumb formula and not necessarily terribly accurate given by a professional miner.
The temperature of the Earth increases 10 deg F per 1,000 feet of depth. Therefore a basement is commonly 52 degrees temperature fahrenheit.
Chart 1. Rule of thumb temperatures at various depths using feet and Fahrenheit.
52 F surface
62 F 1,000 feet
72 F 2,000 feet
82 F 3,000 feet
92 F 4,000 feet
102 F 5,000 feet
112 F 6,000 feet
122 F 7.000 feet
132 F 8,000 feet
142 F 9,000 feet
152 F 10,000 feet
162 F 11,000 feet
172 F 12,000 feet
182 F 13,000 feet
192 F 14,000 feet
202 F 15,000 feet
212 F 16,000 feet
222 F 17,000 feet
To heat a house using this guide, I would have to dig down at least 2,000 feet but more likely 3,000 feet as there is bound to be entrophy and a reduction in temperature. This temperature most likely would be transported by the use of heated water from the 3,000 feet level.
A standard furnace often produces 80 degree vent temperatures to keep the temperature at 68 degrees F.
From a practical stand point, using the 52 degrees F. temperature it is easier to heat from 52 than from the average 20 degrees in winter.
So if we went down a thousand feet we would be increasing the temperature manually about 10 degrees F.
Over the life of a house, say 100 years, that is a considerable utility bill savings.
But let us say we wanted to tap the earth’s temperature to boil water. I suggest an insulated pipe going to 16,000 feet would give you a continuous generation of electricity with a steam engine of some kind. The expense of going that deep is huge. Once such a depth is reached you have pollution free energy forever!
Meaning you have to have a substation controlling the pumping of said hot water.
Potentially such a system would generate enormous amounts of electricity without many side effects to worry about.
The real problem is the density of the water under pressures that deep altering the boiling point of water.
Or you tap into the temperature and transmit the heat to a station underground somewhere in between.
The reward of such a temperature at roughly 16K feet is that you have endless energy to work with at no real expense past getting to that depth.
If we could produce housing at approximately 400 feet below the surface it is not too far fetched that a constant temperature of 62 degrees would make utility heating a thing of the past. You would be heating approximately 5 to 10 degrees F.
In our town there is a river running about 400 feet below the surface. Said water is very hard. Meaning heavy mineral content. But it is useable.
The problem is getting materials capable of dealing with the intense pressures of the Earth at those depths.
God only knows if the temperature rule of thumb will be accurate or if there is a continuous increase above the formula 10 degrees F. per thousand feet.
I think that is relative to where you dig.
The exact engineering might differ considerably the deeper you go.
Water at 400 feet could be under considerable pressure.
The Earth itself is full of various liquids. The entire project may be useless if you run into water wells deep in the earth.
There is also the possibility of huge caverns depending on if Limestone is a factor deep in the Earth. More likely it will be granite. Or Iron deposits.
The amount of knowledge we all ready have from geologists is likely to be invaluable when putting it to practical use.
A comparison with nuclear energy with all of its baggage might make this source of energy more practical than nuclear energy is.
The core of the Earth itself is said to be about the same or higher than our Sun.
So the deeper you go, the chart is possibly inaccurate and the temperature rise is far greater than estimated by the rule of thumb.
We may get the same results at 10,000 feet that we have estimated at 16,000 feet.
We may have to only go 4,000 feet down for the same results in some areas near volcanic activity.
Geothermal energy is practical in places like Iceland.
It may be practical every where else once we know more about heat sources within the planet.