Is it Possible to Produce Any Color Temperature?
For commercial lamps, including incandescent bulbs, the reported color temperature is (or at least should be) a correlated color temperature. So it might not even have the same color coordinates as black body radiation of any temperature. When running on alternating current (AC), the filament of an incandescent bulb cycles its temperature so its effective spectrum is an average over close-to-black-body emission spectra at different temperatures. Running the bulb on direct current (DC) instead of AC may get a bit closer to black body radiation. You can lower the voltage or current to get a lower filament temperature. Tungsten melts at 3695 K.