Using a real oven for this is kind of a massive waste of energy. I got a smallish countertop convection oven and it's basically replaced nearly all uses I previously had for a small toaster oven and our proper mounted oven that takes 8 million years to preheat, along with a good chunk of microwave uses. The big one only gets used for really big stuff now, maybe once every few months at most.
Dunno man, mine takes less then 5 minutes to get to about 150°c. I never measured it but just activating it before I take a pizza from the freezer is enough time to get it fully preheated. It really depends on the quality of the oven i think. There isn't that much more Air to heat so the wasted energy is less then you'd intuitively expect. And regular sandwich irons take at least as much energy, because it's not an enclosed space, consequently bleeding a lot of energy into the room
Your oven is miraculous compared to every fixed oven I've ever had access to.
At any rate we're talking about toast here and an oven broiler only has one setting (usually): all the way on, so you're using as much energy as it takes to brown a steak just to crisp up a bit of bread.
It's not really about heating up the air, anyways, toasters and broilers mostly directly heat things. A toaster (or toaster oven or countertop convection) just has the elements closer so can direct more energy into the bread and less to.. everything else.
Toaster ovens and toasters are at most 1800W appliances. Typical electric oven elements are in the 3000-3500W range. If you're broiling, toaster ovens are much more efficient.
Ovens I've used take roughly 15minutes to warm to 400F (200C), regardless of if they are electric or gas.
If you apply the same anti-consumption calculation to everything in life I applaud you wholeheartedly.
That said, you can buy a toaster oven for $30 from Walmart, and that cost covers the energy, material, transportation, and labour, plus markups at each stage. If you assume a $0.10/kWh energy cost, you might have at absolute most 100kWh of energy used in manufacture. That puts the oven/toasteroven breakeven point from an energy perspective at no more than about 60 hours of heating element usage.
