Porter,
You are describing a physics problem...and you'll need to know a few things about thermal conductivity of the coils and the tank (it will conduct to the earth around it as described).
I would suggest searching:
Thermal Conductivity Equations Formulas Calculator
Thermodynamics and Fourier's Law
I found you a calculator to plug in the numbers:
http://www.ajdesigner.com/phpthermal/thermal_conductivity_equation_heat_transfer_rate.php
It also shows the formulas for solving each of the variables if you know the others.
On nice thing about the calculator is that once you know a couple of the variables...you can play with the length of the tubing.
If physics is a scary thought...might suggest contacting the local university's physics department. In the age of "green" this would make for a great problem for grad student to publish for the craft distilling industry.
Let me know if you find this out.
Cheers,
MJC