Is the temperature of the hottest star's core known? WR 102 is believed to be the hottest star in the observable universe, whose surface temperature is $210,000 ^\circ K$. But the related wikipedia entry does not say anything about the temperature of its core. So,

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*Is the core temperature of this star known?


*Is the core temperature of this star the highest core temperature, as well?
 A: The core temperature of this star isn't known, but can be estimated from theoretical models of stellar evolution, using the observed luminosity and photospheric temperature as constraints.
These suggest that WR102 is currently (it will have lost a lot of mass during its earlier life) about 16 times the mass of the Sun and is probably burning carbon or oxygen in its core (Sander et al. 2019). To accomplish this requires core temperatures of $\sim 10^9$ K. This is a short-lived phase, possibly lasting a few thousand years prior to core collapse and is presumably why WR-O stars are rare (WR102 is one of only a few known in our Galaxy).
It is possible that the star is even closer to core collapse, burning neon or even silicon in its core. This would mean temperatures about 4 times higher still. That is unlikely, because such an evolutionary phase might only last a few days.
So the answer to your question is, probably. Or it could be another of the WR-O stars, such as WR144, which is 3 times as luminous and probably about twice as massive. The hottest core temperature will be in the massive star that is closest in time to ending its life with a core collapse and it isn't possible to securely tell which that is based solely on external appearance.
In particular, surface temperature is not a good guide to core temperature. For example, the red supergiant Betelgeuse is also near the end of its life, probably not quite as close as the WR-O stars, but will have a core temperature that might only be slightly lower. Massive stars of initial masses of 15-30 solar masses will go through red supergiant phases and may be red supergiants (with low surface temperatures) even just prior to core collapse.
