When we pass the current through coil heat generated is calculated by Current^2*Resistance*time.So heat generated in coil depends on current,resistance and time. Like, on which factors heat generated due to spark gap depends??
A coil may also be used as a memory element, as in the normal case, the capacitor. The disadvantage of this arrangement is that I need to calculate in advance what voltage across coil / Gap adjusts. There must be at least the ignition voltage of the electrode array. The stored energy is L / 2 * I² and some are. In the energy components, such as heat losses in the discharge energy to maintain the discharge channel, the loss of the dielectric and the two-foot point energies at the cathode and anode
How big are the anodic and cathodic energy densities are depends, then of the discharge circuit (relaxation generator) and the set current. This means that if you want a specific factor, you must be able to describe the specific electrode assembly parasitic elements.
Your question is not framed clearly. Are you talking about the arc struck between two conductors? Spark and arc are different. Arc is continuous between the two surfaces. Spark is a discontinuous phenomenon.
V=L(di/dt) , L=do/di(variation of flux, with the variation of current). Thus the break down voltage induced across air gap is depends on the inductance of the circuit(coil), and the variation of current(opening time of switch) with time, supplied by battery. Voltage needed for breakdown is higher than the voltage needed, to maintain the spark. Heat generated would be depended on existence(time) of spark, as other effecting factor(media resistance(air gap), heat radiation factor(temp difference etc)) considered constant. Hence longer the duration of spark heat generated would be more.