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

(4) From formula, $\frac{d Q}{d t}=k A \frac{d T}{d x}$

$\Rightarrow k=\frac{\left(\frac{d Q}{d t}\right)}{A\left(\frac{d T}{d x}\right)}$

$[k]=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]}{\left[\mathrm{L}^{2}\right]\left[\mathrm{KL}^{-1}\right]}=\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]$