You're not. Not if you heat your water before putting in the grounds. Practically speaking, once you heat your water, it's a matter of seconds to get the coffee rolling.
Interesting, but I think it's exactly opposite - I would think using water at 4C (the densest water gets) would give you the lowest brew temperature.
With water at 4C, puts the most water inside the pressure chamber, leading to the greatest pressure change for a given delta(T). Instead, if the water is just below boiling, the water going through the grinds must be higher than 100 C (since the pressure raises the boiling point).
It'll brew faster, and there is an argument to be made that quicker brews lead to less burning. But the T would be highest.
If you start with cold water the increasing vapor pressure on the way to boiling will force some of the water through the coffee at varying temperatures, but past that it will reach steady state and end up pushing boiling water. Not sure how much of a difference there is in getting to that point. I don't think pressure matters much since the Bialetti is not a high pressure vessel (maybe 1.5atm probably less if beans are really coarse).
Boiling less quickly (i.e. using lower heat) might put the coffee in contact with boiling water for longer. So it would seem high heat and cold water would be the way to go if you want to minimize the temperature-time product of the beans-to-water contact.
You should try it.