Dimensional formula for thermal conductivity is (here K denotes the temperature) :

Rate of heat flow in steady state in the process of conduction is given by dQdt=kAΔTΔx ⇒k=dQdt(Δx)(ΔT)A⇒[k]=( work )( Time )( Temp )( length )= Force ( Time )( Temp )=MLT-2TK =MLT-3K-1