  Quantum entanglement is fragile to thermal fluctuations, which raises the
question whether finite temperature phase transitions support long-range
entanglement similar to their zero temperature counterparts. Here we use
quantum Monte Carlo simulations to study the third Renyi negativity, a
generalization of entanglement negativity, as a proxy of mixed-state
entanglement in the 2D transverse field Ising model across its finite
temperature phase transition. We find that the area-law coefficient of the
Renyi negativity is singular across the transition, while its subleading
constant is zero within the statistical error. This indicates that the
entanglement is short-ranged at the critical point despite a divergent
correlation length. Renyi negativity in several exactly solvable models also
shows qualitative similarities to that in the 2D transverse field Ising model.
