# Heat loss in a cylinder (e.g. electrical wire)

Conceptionally there are things I'm not sure of in heat transfer, which I hope you can help me with.

Say for instance we have a long electrical wire with a uniform temperature distribution (higher temperature than ambient air). Because of the temperature difference, there will be a constant heat loss per unit length (W/m). Now in case, you insulate this wire, what do you actually do? The same heat has to escape? So as I understand, the only thing you do is slowing down the heat initially (depending on the thermal conduction in the material) and increasing the surface area so the heat loss per unit area (W/m^2) will decrease, but in steady state will the heat loss per unit length not be the same?

However, assuming that the wire is a metal, the rise in temperature will increase the resistance of the wire. If the current through the wire is kept constant, then the rate at which heat is generated (i.e., $I^2R$) will be larger than before. If the voltage across the wire is kept constant, then the rate at which heat is generated (i.e., $\frac{V^2}{R}$) will be smaller than before.