Thermal Contact Conductance

What is the meaning of thermal conductance defined in contact? What is the program controlled Thermal conductance value? How to achieve partial conductance through the contact? 

It represents thermal conduction through the contact.

q=TCC(Tc-Tt)

Theoretically, TCC=infinity would represent perfect contact.
Thus, Tc=Tt for TCC=infinity.

However, if user defines too large a TCC value, it will create numerical instability issues. So, the default calculation is an attempt to come up with a large enough value for TCC to simulate "perfect" thermal contact without causing numerical instability. 
 
Partial thermal contact can be achieved by throttling TCC down to a small value. As TCC gets smaller, the Delta Temp between contact and target surfaces should increase. As TCC approaches zero, q=zero and the interfaces approaches a perfectly insulated condition with no heat transfer.