I think there won't be any heat generated other than spark gap. even at the spark gap too heat wont sustain because the dielectric does it work there (cooling).. small amount of heat may be generated in the wire drum due to friction...
The conservation of energy principle also applies to the WEDM.
Thus, I have over the wire and through the contact points of the wire a loss of energy, one can even calculate. Looking at the overall energy balance that is necessary, the energy shares the biggest shares are at the electrodes foot points and in the discharge channel, of course. The two energy components mentioned above are for example responsible for a possible broken wire. Much of this heat is dissipated by the cooling system and then can not lead to the negative phenomena, such as wire breakage.
If you have to find a source, there is a negligible amount of head dissipation on the wire due to current passing through.
The discharging process is highly transient & in micro scale. I doubt any direct measurement approach is useful. Energy in EDM is often measured by recording the waveform of voltage and current across electrodes and calculating using ohm's law. However, that's only the input energy to the process. It wouldn't be very useful without knowing how energy-efficient is the process and the percentage of energy that goes to the tool and workpiece or dissipated. Studying material removal amount on both electrodes afterwards can be an indication of how much energy went into each eletrode.