The thermodynamic equilibrium in a system of randomly quantized vortices in superfluid helium with counterflow between the normal and superfluid components is considered. Both continuum and discrete approaches are studied. Even when using the continuum approach for the system as a whole, the partition function for the various vortex loop configurations can only be calculated by involving the discrete approach. It is obvious that discretization is important to numerical studies. Numerical simulation is the main tool for solving the stochastic dynamics of quantum vortex filaments subject to random force, due to their complexity. Some physical consequences of the results are discussed.