This study used the finite element method to investigate the acoustic bandgap (ABG) characteristics of three-dimensional pentamode metamaterial (PM) structures under the thermal environment, and a method for controlling the PM ABG based on external temperature variation is also proposed. The results indicate that the complete acoustic bandgap can be obtained for a PM in the thermal environment, which makes the PM combine the bandgap characteristics of phononic crystals. More than that, the bandwidth and locations of ABGs can be effectively manipulated by controlling the temperature. Considering the softening effect of thermal stresses, the ABG gradually moves to lower frequencies as the temperature increases. Based on this, different degrees of ABG tunability can be achieved by changing the thermal environment to propagate or suppress acoustic waves of different frequencies. This work provides the possibility for PMs to realize intelligent regulation of the bandgap.