  Using state of the art tensor network computations combined with spin wave
theory, we compute the finite temperature phase diagram of the spin 1/2
$J_1-J_2$ Heisenberg model on the square lattice with ferromagnetic $J_1 < 0$
and antiferromagnetic $J_2 > 0$. We localize the first order line originating
from the first order zero temperature point as well as the second order thermal
transition at large $J_2$ associated with spontaneous lattice rotation symmetry
breaking. This second order line terminates at a critical end point where it
meets the first order line. We found no evidence for an intermediate phase.
