This paper presents the design of a multivariable temperature control for a refrigeration system based on va-por compression employing an internal model control (IMC) technique. The refrigeration system is based on the PID18 benchmark, which is a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2 \times 2$</tex> MIMO system. The system is identified using a Box-Jenkins model and the relative gain array is calculated to determinate the best variables to be paired. IMC controller is evaluated using a set of quantitative performance indices. Obtained results shows that the proposed IMC controller improves the system performance compared with the baseline method presented in the the PID18 Benchmark challenge.