Effect of Vacuum on Heating rate

I haven't done the sums, but I suspect the time difference would be practically immeasurable.

Anything that takes 40kW for 1 hr to get to 1000°C is going to have a thermal capacity many, many times greater that 1 m³ of air at 1 atm.

(I assume you're talking about measuring the chamber temperature at the inner surface of the walls).

with only radiant heat to heat the object the rate of heating will be a function of the surface emissivity of the object. Shiny stuff takes a lot longer than pieces of carbon.

WHat are you heating?

If you pull a vacuum on the chamber you will heat by radiation and conductiviy and will loose all convective heating. Convective heating helps to even the heat much faster.

Radiatiive and conductive heating will be unchanged, bu tconvective heating will be nonexistent under vacuum.

The heat capacity of the gas is negligible in the system you described, so the heat energy requiredinput will be unchanged.

AT that temp, most of the heat transfer is probably radiation at the end of the heat-up, but not at the start. The heated source will get hotter than before, and will get hot faster. The heated parts will not begin to heat up until the radiator is closer to its terminal temperature.

If view factors and emmissivity are not uniform, hot spots will be much more pronounced when you lose convective heating.

Unless you have a furnace and heaters designed for operation in a vacuum, you will burn up the heaters. Heating elements must reject heat to either air, a liquid, or a solid. Placing any heater in a vacuum will prevent it from rejecting the power and will become incandesent and will burn out.