The problem of determining the routes of vehicles engaged in the logistics of the cold chain (CCVRP), involves multiple considerations such as transportation costs, product loss costs, and refrigeration costs. How to reduce operational costs has become a pressing practical issue for enterprises. To address the CCVRP under uncertain demand and with a heterogeneous fleet, the BPR road impedance function is employed to calculate road travel time, and a Wasserstein distance-based distributionally robust optimization approach is adopted to handle demand uncertainty. The CCVRP model incorporating road impedance and demand uncertainty was constructed, with the objective function being to minimize total cost. This was achieved by comprehensively considering constraints such as customer service levels, route continuity, load capacity, and goods flow balance. Taking the classic Sioux-Falls transportation network as a case study, numerical experiments were conducted using Gurobi to solve both the certain and uncertain demand models. The results indicate that the total costs achieved by the uncertain demand model are 5.8% lower than those of the certain demand model.