I remember something similar came up in discussion on a completely unrelated subject a while back. Something to the effect of: is a horrible, shameful old school 100 watt incandescent light bulb really bad? From the light producing perspective, only 5% of energy is converted to light. But where does the 95% 'wasted' energy go? Heat. On a cold winter day I am burning natural gas in my furnace to create what? Heat. Hmmm so from the light ONLY perspective, low energy LEDS are good. But from the light PLUS heat perspective, maybe the oldies aren't so bad. But I digress...
This wasn't the web site, but it was one like it.
https://www.quora.com/How-much-ener...-temperature-of-an-average-room-by-10-degrees
So I took the sample calculation, verified I got the same answer & scaled it to your hot box. It shows very little heat (like 5 x 100 watt light bulbs worth) will raise ambient air to toasty 200C in no time flat. But like some of the subsequent posts in the link & what I recall of the 'environmental' discussion, its not that simple a calculation. It assumes perfect insulation and only heating the dead air, not the contents like your parts which are dense mass metal.
So maybe another way of guestimating is a kitchen oven. They are about 5 cubic feet ~0.14m3 volume. I've read about 5000 watts capacity, assuming that at highest dial temp which is about 250C. That equates to about 35,000 watts per m3 volume. (Notice way higher than the air only calc for only another 50C temp). I guess that's why there is a big ass electrical plug on the back. I'm not sure what your target temp is, but you can probably proportionately scale it all things equal. Lower watts might be ok, but the wait time goes up. It may not be a trivial amount of power and insulation is important.
Just for interest on the high temp spectrum, example heat treat oven rated at 1200C (2200F) with internal volume of 0.006 m3 (0.22CF) uses 1560 watts which is 250,000 watts per m3 volume.
https://www.soulceramics.com/collections/knife-ovens/products/evenheat-knife-oven-kh-414