Temperature Profile in Pipe due to Soil

[SuperG]

What (or where) are the equations for heat transfer between fluid-pipe-soil?

I have a pipeline simulator and am determining the temperature decline of a gas. The pipeline is buried 3' under the soil line and the soil line is 100' under water. As I run the model with decreasing flow rate, I found the temperature drops slowly until about a 40% drop in flow rate. Then the temperature drops a little more rapidly. What determines this threshold?

I also assumed no significant outer wrap...