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A network of driven nonlinear oscillators without dissipation has recentlybeen proposed for solving combinatorial optimization problems via quantumadiabatic evolution through its bifurcation point. Here we investigate thebehavior of the quantum bifurcation machine in the presence of dissipation. Ournumerical study suggests that the output probability distribution of thedissipative quantum bifurcation machine is Boltzmann-like, where the energy inthe Boltzmann distribution corresponds to the cost function of the optimizationproblem. We explain the Boltzmann distribution by generalizing the concept ofquantum heating in a single oscillator to the case of multiple coupledoscillators. The present result also suggests that such driven dissipativenonlinear oscillator networks can be applied to Boltzmann sampling, which isused, e.g., for Boltzmann machine learning in the field of artificialintelligence.