It varies linearly with temperature and is affected by polarity and hydrogen bonding of the molecules.
The th. conductivity, K, of most mineral and synthetic hydrocarbon lubes is in the range between 0.14 W/(m.K) at 0 deg C to 0.11 W/(m.K) at 400 deg C.
For a rough estimation one can use:
K = (0.12/s) (1-1.667 [θ]/10,000)
where s, specific gravity at 60 deg F; [θ] is the temperature in deg C.