How does the temperature of a newly formed neutron star core stabilize shortly after collapse?

It cools rapidly, stabilizing perhaps around $100$ million K ($10^8 ext{ K}$)

Although a neutron star core is born incredibly hot, reaching initial temperatures near $10^{11} ext{ K}$ from the rapid gravitational energy release, this state is transient. These remnants begin to cool quickly over a relatively short astronomical timescale. The initial heat dissipates significantly, leading to a stabilization point estimated around $100$ million Kelvin, or $10^8 ext{ K}$. While this stabilized temperature is much hotter than the Sun's operating temperature, it is a measure of residual heat, not a sustained, self-regulating temperature maintained by ongoing fusion, meaning even older neutron stars will eventually radiate away most of this initial thermal energy.