The elevated level of public and organizations awareness concerning sustainability has necessitated the adoption of environmentally conscious practices in the management of supply chains. As such, classical inventory models wherein the sole measure of performance is cost minimization are no longer appropriate to handle such emerging and pressing issue. This paper assesses the impact of accounting for carbon emissions, resulting from transportation and storage activities of a cold item, in the context of a multi stage supply chain comprised of a plant/warehouse, a distribution center (DC) and a retailer. We present an operational cost minimization model, a carbon footprint minimization model and a hybrid economic and environmental minimization model where all models seek to determine the optimal lot sizing and shipping quantities, alongside the number of trucks to be used in the upstream and downstream directions of the supply chain as well as the number of freezer units utilized at the DC which is owned by a third party logistics provider. The structural properties for the optimal solution of the three models are identified and solution algorithms are also proposed. Upon conducting computational experiments, it turns out that the incorporation of carbon related costs, through carbon tax regulation, may call for adjusting the adopted operational policy which results in a minor increase in the operational cost. However, this increase is outweighed by the savings resulting from the carbon related costs. Numerical results of the sensitivity analysis on the carbon tax policy indicate that as the tax rate increases, substantial reductions in the amount of carbon footprint emitted are realized and cost savings are also achieved when adopting the lot sizing and shipping policy of the third/integrated model over the operational cost minimization model.