Substituting dimensions for corresponding quantities in the relation having
coefficient of thermal conductivity.
Heat $ΔQ$ transferred through a rod of length $L$ and area $A$ in time $\Delta t$
$\Delta Q = KA \left(\frac{T_{1} -T_{2}}{L}\right) \Delta t$
where $K = $ coefficient of thermal conductivity,
$T_1 -T_2 =$ temperature different .
$\therefore k =\frac{\Delta Q \times L}{A\left(T_{1} - T_{2}\right) \Delta t} \quad ...\left(i\right)$
Substituting dimensions for corresponding quantities in Eq. $\left(i\right)$, we have
$\left[K\right] = \frac{\left[ML^{2}T^{-2}\right]\left[L\right]}{\left[L^{2}\right]\left[\theta\right]\left[T\right]}$
$= \left[MLT^{-3}\theta^{-1}\right]$