Why are protein hydrophobic cores denatured by heat when entropic forces should be favoured at high temperature
You are correct that the hydrophobic interactions are stabilized at higher temperatures. However, I believe the addition of heat mainly disrupts protein structure by breaking hydrogen bonds through increased thermal motion. 

Once the secondary structure starts to go, any tertiary interactions will get scrambled, likely resulting in the separation of hydrophobic residues. The refolding of the polypeptide backbone must be stronger than the enhanced hydrophobic interactions.