The temperature of a plug whether "Hotter" or Colder" type is the same at start up. The temperature is based on operating temps so it would have no effect for an initial cold start up.
I disagree here is a great post that explains it.
The dude who posted this engineers ignition systems.
"I'm going to have to jump in here real quick and comment on heat range and cold starting. Heat range has EVERYTHING to do with cold starts. Look at it this way...if we weren't worried about cold starts and fouling, we'd just put stone cold plugs in everything for maximum protection against preignition and call it good.
Hotter plugs have longer ceramic tips; think of tip length as the length of the path to the heatsink (cylinder head). Cold plugs have short tips to dissipate the heat quickly. It's that physical length that's so important because it represents what we call the "shunt path". In other words, the resistance along the insulator tip determines whether it's easier to conduct ignition current across the gap or along the insulator to ground. A new or plug at operating temperature has a shunt resistance that's basically infinite. When an engine is starting, and the mixture is enriched, and fuel and soot are distributed on the insulator. These deposits are conductive, dropping the resistance of the insulator surface and potentially allowing current flow to ground - up inside the spark plug. Once the insulator is shunted, the current flows along the insulator to ground, and there's no spark in the gap (so most likely no start).
Spark gap is critical to cold starting as well. Colder plugs must use smaller gaps, hotter plugs can use larger gaps since their shunt path is longer. That's why worn plugs start misfiring, the gap resistance becomes higher than the shunt resistance, so the current doesn't always flow through the gap. Using a wider gap on a colder plug will have you misfiring quickly during a cold start, or not starting at all. Conversely, wider gaps on hotter plugs (to a point) make for easier starting because the fuel won't foul the gap as easily, and it's statistically more likely to get a combustible mixture in between a larger electrode gap...but you've got to have the tip length to support the gap. There's a lot more to it, but that's the nickel version. It also has to do with voltage drops along the circuit, with higher energy deliveries being at the points of greatest voltage drop. Consider the drops along the way at the spark plug suppression resistor, terminations, etc.
There is no operating of an engine requiring more "demand voltage" than cold starting. This is because the voltage required to stimulate electron flow across the gap is higher when the metals are coldest. This pretty much limits spark gap since if we go too far and there isn't enough voltage available to break down, or ionize, the gap we probably don't start. Cold starting can use all the ignition voltage you have available, especially when you consider that battery voltage is lower, and dropped further by the current draw of the cranking motor, etc. And there's quenching...energy drawn from the gap byy the relatively cold surroundings. Kind of like lighting a cold fireplace compared to re-lighting one that's already hot but out of wood...it lights much easier warm (takes less ENERGY). There's a lot more to it, and I can answer questions if needed. 20+ years engineering ignition systems and spark plugs."
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