Here we show how the temperature profile varies in a plane wall with convection. Temperatures become almost constant with respect to position for Biot number Bi$=hL/k < 0.1$.
$\theta * = \frac{T-T_a}{T_i-T_a}$
This calculation is based on Section 5.5.1 of Bergman et al, "Fundamentals of Heat and Mass Transfer" 8th Ed.