One Dimensional or Two-dimensional Heat Conduction

if it's steady state convection will be equal to conduction. in that case you can ignore thickness and just use surface area for heat loss calculation.

kaiser

Actually you have 2D analysis since you should be interested in evenly warmed surface and you will need to add energy at some points.

If you are not looking for energy accumulation (time dependent) thickness is neglible, if inertial effects are important, then mass (and thus thicknes) need to go into your analysis