The osmotic second virial coefficient A2 of nonathermal polymer solutions is discussed for a simple lattice model. Each molecule (n-mer) corresponds to a self-avoiding walk of n - 1 steps on the simple cubic lattice and each intrachain or interchain contact contributes a quantity - e to the energy of the system. The function A2(n,f) where f = exp(e/kT) is obtained exactly by direct counting for n ≤ 6 and is evaluated approximately by a Monte Carlo technique for higher n values up to n = 40. In the asymptotic limit n → ∞, it appears that the theta temperature (defined by A2 = 0) is given by kθ/e ≃ 3.71 (fθ ≃ 1.309) while the quantity (dA2/d ln f)θ seems to remain different from zero. Two different theories of polymer solutions are briefly compared to these results.