Correct. The ground is a MASSIVE heat sink, but can only absorb and transmit heat so quickly (how much thermal conductivity it has; just the mathematical reciprocal of insulation/resistance). Having a large contact area and/or water helps a lot. If you can get down to the ground’s natural/ambient water table, it’ll conduct a lot better than dry dirt and rock (not to mention that evaporation can help with sufficient air flow).

If you make use of flowing water, probably it’s just going to be a matter of the temperature of the source of water, as it’ll likely eclipse (depending on rate and volume of flow) what gets absorbed by the ground. Unless it’s a closed loop, in which case you’re essentially just increasing the surface area of ground you’re transmitting to (and you’ll need to take advantage of convective flows like with the air, or you’ll have to actively pump to keep the flow going).