How to convert BTU into degrees?

As you say, there isn't a direct conversion. That's because it will depend on many things, such as how much of that energy is going into the metal, and how much of the energy is being radiated away from the metal. Putting the metal object on a large metal table would be a bad idea for instance. Such a table is called a "heat sink" because it draws heat away from things.

The more it is exposed to air currents and the open lower-temperature air, the more heat will be lost that way too. That says to me that you want some kind of enclosure that can stand these high temperatures, although if there are fumes being given off maybe you need to have some sort of venting for safety.

About the only calculation I can do is the energy naturally radiated away from a 600 F object. That's 589 K. According to the Stefan-Boltzmann Law, such an object radiates (5.67x10^-8)(589^4) = 6824 Watts per square meter of surface area. (The more surface, the more heat loss). A BTU is pretty close to a kJ/sec (1000 W), so that's about 6.8 BTU per second per square meter or 24,000 BTU per hour.

So not 600 F if you've got a square meter of surface area. But if you do the same calculation at 400 F, that's only 43% of the energy or about 10,000 BTU/hr. So you're in the right ball park, especially if your surface area is a lot smaller than 1 m^2.