You should take a look a non-dimensional number called the Brinkmann Number. It gives an indication of how important is the heat produced by viscous dissipation compared to the heat that gets transferred via molecular conduction. You can calculate the Brinkmann Number as
Br = mu * U_e^2 / (k * delta_T)
Here, delta_T represents the temperature difference in the system.
If Br > 1, viscous dissipation effects must be included in the fluid flow analysis.