The Hertzsprung-Russell (H-R) diagram is a scatter plot that shows the relationship between the luminosity and temperature (or spectral class) of stars. In this diagram, stars are typically plotted with temperature on the horizontal axis (increasing from right to left) and luminosity on the vertical axis (increasing upwards).
A white dwarf is a stellar remnant that has exhausted the nuclear fuel in its core and has lost its outer layers, leaving a hot core exposed. As it cools over time, it will transition through different temperatures, eventually becoming a cooler object.
A white dwarf with a temperature of around 10,000 Kelvin would generally fall into the region of the H-R diagram that corresponds to white dwarfs, which are typically found in the lower left portion. In terms of spectral classes, a temperature of 10,000 K correlates with a spectral type of approximately DA (hydrogen-rich) or DB (helium-rich), depending on its composition.
In summary, a white dwarf at 10,000 K would be found in the lower left region of the H-R diagram, likely corresponding to spectral classes DA or DB.