The SA (Simulated Annealing) is a meta-heuristic to combinatorial and optimization problems. The main purpose here is to investigate several cooling schedules (main parameter of SA) combined with Constructal Design for geometric optimization of an isothermal Y-shaped cavity intruded into a solid conducting wall with internal heat generation. This shape was optimized with Exhaustive Search and Genetic Algorithm in previous studies of literature. The problem has four degrees of freedom (H/L, L-1/L-0, t(1)/t(0), alpha) and two constraints: the cavity and auxiliary fraction cavity areas (phi and psi). Five different cooling schedules are evaluated: Fast, Exponential, Boltz, BoltzExp and ConstExp1. The first three methods are default, while the others are hybrid proposed here. Firstly, it is evaluated the percentage of simulations in which the global optimal point is achieved for the case with square solid wall. Algorithms hybrid and Fast lead to the highest and lowest reliabilities to find global optimal geometries. Posteriorly, a complete optimization of the Y-shaped cavity evaluating the effect of constraints phi and psi over four times optimized Y-shaped cavity are performed. Results are compared with those previously obtained with GA (Genetic Algorithm). The combination of the best cooling schedules improves even more the achievement of the global optimal shapes. (C) 2015 Elsevier Ltd. All rights reserved.