New field content beyond that of the standard model of particle physics can alter the thermal history of electroweak symmetry breaking in the early Universe. In particular, the symmetry breaking may have occurred through a sequence of successive phase transitions. We study the thermodynamics of such a scenario in a real triplet extension of the standard model, using nonperturbative lattice simulations. Two-step electroweak phase transition is found to occur in a narrow region of allowed parameter space with the second transition always being first order. The first transition into the phase of nonvanishing triplet vacuum expectation value is first order in a non-negligible portion of the two-step parameter space. A comparison with two-loop perturbative calculation is provided and significant discrepancies with the nonperturbative results are identified.