By Using the Monte Carlo renormalization group method we have calculated the critical exponents β/ ν and ν for the (2 + 1)-dimensional Z(2) lattice gauge model at finite temperatures. The numerical investigation is based on Binder's procedure with up to 1.5 million updates per variable at given coupling constant. In accordance with the conjecture of Svetitsky and Yaffe the critical exponent ν turns out to be unity. The value of β/ ν, however, shows a dependence on the number of lattice points in the temperature direction. With increasing number of lattice points it tends to become larger than the conjectured value of 1 8 .