The concept of a "recombined universe" and its "core" temperature is not a recognized scientific concept within our current understanding of the universe. It's important to note that the term "recombination" is typically used in the context of the early universe, specifically referring to the epoch when electrons and protons combined to form neutral hydrogen atoms, allowing light to travel more freely.
During this recombination epoch, the temperature of the universe was estimated to be around 3000 Kelvin (K), which corresponds to the Cosmic Microwave Background (CMB) radiation we observe today. However, the notion of a "core" temperature for the entire universe does not apply, as the universe doesn't have a distinct core in the conventional sense.
The universe is considered to be homogeneous and isotropic on large scales, meaning that its properties, including temperature, are relatively uniform throughout. It is important to distinguish between the temperature of the cosmic background radiation and the temperature of specific objects or regions within the universe, which can vary significantly.
If you are referring to the temperature of a specific object within the universe, it would depend on various factors such as its size, composition, and the energy sources acting upon it.