Actually, let me change my mind. This isn't a "thermal equilibrium" problem - the air temperature, boot surface temperature, and the mold-able gel (or whatever) temperature are all different, so the way you measure the temperature matters.
AFAIK, Jackson doesn't give instructions on the temperature the boot (or more specifically, the molded gel or whatever within the boot) should reach, although that is what matters. They give instructions on what temperature the air of a hockey-style convection oven should reach, and how long the boots should stay in that oven, in order to get the molded gel to the desired temperature.
Without the fancy professional oven, maybe the best we can do is guess by feel. Doing it that way, it makes sense to play it a little safe - you want it hot enough to just start to be mold-able, but no hotter. What the thermometer can do is tell you if it gets way too hot. I.E., the stated oven temperature is too hot for the surface of the boot to reach - but by then, the boot may already be damaged.
If the boot maker provides the name of a pro who can do the work, that's likely the safest best, because if something goes wrong, as it may, they will probably warranty it. It doesn't matter whether the pro is a "figure skating pro shop", a hockey or roller skate shop, a ski shop, or a housewife who works out of her basement using a heat gun - a competent pro is a competent pro, and the boot companies all make a point of figuring out who they trust to do good work on their boots. AFAIK, all the reputable boot makers will make good on problems their recommended pros create, or the pro likely will - though you can ask ahead of time.
P.S. Before someone complains, when I say a competent pro is a competent pro, I assume that your boot maker recommends them.