We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest (J₁) and next-nearest (J₂) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for J₂/J₁ > 1/2 , thermal fluctuations give rise to an effective Z₂ symmetry leading to a finite-temperature phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that T_c  tends to 0 with an infinite slope when J₂/J₁ tends to 1/2.