K is not necessarily related to the properties of the bodies coming into contact, 
but instead is the property of a fluid (imaginary or not) which fills the gap between 
the bodies.  Please note dependence of h on lgap as mentioned in the Remarks of 
*CONTACT_..._THERMAL, viz

h = H0           for 0 <= lgap <= LMIN
  = hcond + hrad for LMIN < lgap <= LMAX 
  = 0            for lgap > LMAX

When in intimate contact (i.e., lgap < LMIN), we want strong heat transfer conductance 
between the two bodies.  But, understand that transferring heat across the gap relies 
on a penalty-based numerical method where H0 can be thought of as a penalty scale factor 
which has dimensions.  If H0 is set arbitrarily high you will induce numerical instabilities, 
so H0 must be chosen carefully.  To attribute some physical meaning to H0 we often set it to 
the that of boiling water, i.e, H0=10,000 for SI units. 

With all of that in mind you might represent the fluid in the open gap with the 
conductivity (K) of air,  or water, or perhaps the average of the conductivities of the 
two bodies.  The best choice is the one that makes most sense to the analyst.

Note that when we know the bodies will always be in contact (no gaps at the interface) 
we typically set LMIN=LMAX = 0.1 * element size.  Then, it's either H0 or zero 
(if there happens to be a gap), i.e., K/GAP is ignored.
 
ts
Ticket 2016022210000041