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Changes in mortality rates have an impact on the life insurance industry, the financial sector (as a significant proportion of the financial markets is driven by pension funds), governmental agencies, and decision makers and policymakers. Thus the pricing of financial, pension and insurance products that are contingent upon survival or death and which is related to the accuracy of central mortality rates is of key importance. Recently, a temperature-related mortality (TRM) model was proposed by Seklecka et al. (Journal of Forecasting, 2017, 36(7), 824-841), and it has shown evidence of outperformance compared with the Lee and Carter (Journal of the American Statistical Association, 1992, 87, 659-671) model and several others of its extensions, when mortality-experience data from the UK are used. There is a need for awareness, when fitting the TRM model, of model risk when assessing longevity-related liabilities, especially when pricing long-term annuities and pensions. In this paper, the impact of uncertainty on the various parameters involved in the model is examined. We demonstrate a number of ways to quantify model risk in the estimation of the temperature-related parameters, the choice of the forecasting methodology, the structures of actuarial products chosen (e.g., annuity, endowment and life insurance), and the actuarial reserve. Finally, several tables and figures illustrate the main findings of this paper.