In principle, Jack, the temperature in the spark gap should reflect the intensity (rate) of energy discharge, which will be voltage times current. However there can in theory be complications. A more conductive gas (compared with pure ionised air) might result in a lower voltage and higher current, with less ionisation, meaning a partial short circuit compared with having to discharge the energy through ionised air. I speculate that this is what the Briggs note refers to when it says that the spark will be orange in the presence of sodium.
In the old days people used to do a sort of party trick, striking a continuous arc between two electrodes then blowing compressed air across the gap. The arc would then take a long curved path across the gap, following the position of the displaced ionised air. This is because it takes a lot more voltage to strike an arc through cool air, than it does to maintain one through ionised air.
I don't have any data on colour versus intensity: is an intense arc white or blue? I think the answer is our eyes can't see far enough into the violet to observe the true colour anyway.
With regard to the sound of a spark, in my experience arcs are noisy, and an arc welder at high current is a whole lot noisier than a spark plug. For sound to reach us, the spark has to have had some duration. If you integrate voltage times current with respect to time, you have the amount of energy discharged. In other words volts times amps is power, or the rate of energy discharge. Volts times amps summed up over time is energy. Or, volts times amps is power, in watts. Kilovolts times amps is kilowatts. Kilowatts times time is kilowatt hours, which is what the electricity company charges you for on your bill.
A standard Kettering ignition system stores energy in a magnetic field, then with the aid of a capacitor, turns that energy into a spark over whatever duration it takes to use it all up. It is possible to create a much hotter spark with a lot less energy, just by reducing the duration of the spark. More kilowatts will flow, but very briefly. That is what a Capacitive Discharge Ignition does: it produces a very intense, very brief spark compared with a Kettering system. Which is better? Depends what you are trying to do. Combustible gas is ignited by raising the temperature of a large enough amount of gas, to a sufficient extent. CDI is marvellous for firing across fouled plugs, but it is poor for igniting lean mixture, because of the short duration.
Getting back to your point, I think the amount of sound you get from a spark depends on the energy discharged rather than the rate of discharge (the spark intensity). My recollection is that CDI sparks are quieter than Kettering sparks - but I haven't really tested this.
I'll repeat a point I've made in another thread. My father and uncle, a pair of vintage racing car enthusiasts, had a problem choosing an ignition system for an old 2 stroke that was very difficult to keep firing because it fouled its plugs. They tried Kettering and found it ran very well until the plugs fouled. They considered CDI but were alarmed to find that if you put a sheet of paper in the spark gap and continuously triggered a spark, the CDI system would just burn a microscopic hole in the paper. The original Kettering system, in the same test, immediately set fire to the paper. So, you can't have it both ways. They experimented and found a CDI system that blackened more paper than the other CDI system they tried, and settled for that. It worked well enough: they never fouled another plug.
