There are two important equations: Power = Volts * Amps Volts = Amps * Ohms Substituting these in you get Power (dissipated) = Current ^2 * R

This means for a given contact resistance, the energy dissipated as heat into that contact is proportional to the square of current. Note, however, that you can increase the power also by increasing voltage, and not needing lower resistance contacts. That is why laptop chargers are usually 19V, and power transmission lines are 500-750kV.