I'm shocked, shocked! to see an SI stickler like you accept such a travesty of the One True Righteous Standard Nomenclature. ;)
It is, of course, Wm^-1K^-1. Isn't that clearer?
We slipshod ambi-unitary folk often just write W/m/K, which (besides being much easier to read) has the advantage of obeying standard math notation, unlike the watts per millikelvin version.
Cheers
Phil Hobbs