Go as deep as you can get away with.

A thermocline is a type of thermal layer that has a sharp temperature gradient across it to deal with large temp differences between thermal layers, and as such it tends to move and have a 'current' due to density and energy issues etc.

The thermal layering and thermoclines mentioned in ground HVAC talk is not about water, but mostly about getting down below frost lines and to where the soil is warmer to be able to hold or extract heat. Systems like that are mostly hype and are not efficient long term unless another heat source is nearby such as a vent, large sewer pipe (heated by all the homes and buildings feeding it with water and air), or hot springs.
I have heard of folks digging a hole around a large sewer main and wrapping a coil or tubing around it, and heat shield around that, and reclaiming the heat lost there to heat their home. Now THAT is efficiency, using everyone else's poop habits to heat your home instead of fuel or energy! You can always count on people being full of 'it' so you know you have a reliable heat source there. If your house gets cold just take all your neighbors brownies with laxative and wait an hour or so.

If you live in cold weather the deeper you go the lower your heating bill will be per gallon, and the less likely a freeze becomes.