In this paper, we introduce a class of the multiplicative tempered fractional integral operators. Then, we investigate two Hermite–Hadamard type inequalities for this class. By using the established identity and the multiplicative convexity, we establish some integral inequalities for the multiplicative tempered fractional integrals involving the $ \lambda $-incomplete gamma functions. And our results obtained in the present paper generalize some results given by Budak and Tunç (2020) and Ali et al. (2019). Also, we provide three examples to demonstrate the simplicities of the calculations.