In this study, the characteristics of heat transfer and flow in helically corrugated helical tubes are investigated. Numerical calculations are carried out to study the influence of different corrugation depths and corrugation pitches on the Nusselt number and friction coefficient, considering a mass flow rate range of 0.75–1 kg/s. The results indicate that the sudden change in the flow velocity generated by the corrugated structure and the secondary flow generated by the helical structure improve both heat transfer efficiency and flow resistance. Furthermore, the Quasi-Monte Carlo method is employed to calculate the heat transfer reliability when the structural parameters and mass flow rates are regarded as random variables in practical engineering. To improve the calculation efficiency, the Kriging model is proposed to replace the numerical calculation process for predicting the Nusselt number. The results demonstrated that the Kriging model has high accuracy and efficiency in predicting the Nusselt number and calculating the heat transfer reliability. When the mean values of corrugation depth, corrugation pitch, inlet diameter, and mass flow rate are 1.5 mm, 32 mm, 16 mm, and 0.85 kg/s, respectively, the heat transfer reliability of the helically corrugated helical tube was found to be 99.28% under the condition that the error limit is 7.5% of the mean value.