Using an SU(2) invariant finite-temperature tensor network algorithm, we provide strong numerical evidence in favor of an Ising transition in the collinear phase of the spin-1/2 J(1)-J(2) Heisenberg model on the square lattice. In units of J(2), the critical temperature reaches a maximal value of T-c/J(2 )similar or equal to 0.18 around J(2)/J(1) similar or equal to 1.0. It is strongly suppressed upon approaching the zero-temperature boundary of the collinear phase J(2)/J(1 )similar or equal to 0.6, and it vanishes as 1/log(J(2)/J(1)) in the large J(2)/J(1) limit, as predicted by Chandra et al., [Phys. Rev. Lett. 64, 88 (1990)]. Enforcing the SU(2) symmetry is crucial to avoid the artifact of finite-temperature SU(2) symmetry breaking of U(1) algorithms, opening new perspectives in the investigation of the thermal properties of quantum Heisenberg antiferromagnets.