The deterioration of a shot sleeve in squeeze casting due to thermo-mechanical fatigue often results in lowering the reliability and availability of the squeeze casting machine, thus reducing its productivity, meanwhile increasing the life-cycle maintenance cost. This paper presents an efficient Bayesian kriging meta-modeling method for spatiotemporal prediction under data uncertainty and non-normality, with the target applications for controlling the deformation, optimizing machine design, and predicting component fatigue cracking thus improving the reliability and availability of mechanical system. Spatiotemporal kriging model is established to substitute the complicated computer model by using numerically simulated data. Bayesian probabilistic approach is then developed to quantitatively evaluate the validity and predictive capacity of kriging meta-model, considering data uncertainty. The Anderson-Darling goodness-of-fit test is employed to perform the normality hypothesis test of difference values of validation data. Box-Cox transformation method is utilized to convert the non-normality data with the purpose of facilitating the overall validation assessment of meta-models with higher accuracy. Bayesian confidence measure is presented to quantify the confidence on the predictive capacity of the kriging meta-models, given the transformed data. A procedure is proposed to implement the proposed probabilistic methodology for meta-modeling and model validation with non-normality response series. The impact of data normality assumption and decision threshold parameter in quantitative model assessment is also investigated by using Bayesian inference approach. The effectiveness of the proposed methodology and procedure is demonstrated with the spatiotemporal temperature prediction in squeeze casting.