Progressive cavity pumps (PCP), which uses the ordinary nitrile rubber, are widely used in heavy oil production, and it is prone to failure of the core-burning perforation of the stator bushing. The expensive hydrogenated nitrile rubber is resistant to high temperatures but does not have precise use depth and cross-sectional parameters. In order to solve above problems, first of all, the rubber hyperplastic constitutive model of ordinary nitrile rubber and hydrogenated nitrile rubber is fitted based on the thermal aging and tensile tests. And then, a new finite element model is established based on the one-way decoupling method to decompose the delayed heat generation phenomenon. Finally, the influences of working well depth, interference, and wall thickness on the lagging heat generation are studied, and the orthogonal table of the three factors is listed. The research results show that ordinary nitrile rubber is better than hydrogenated nitrile in working temperature below 70 ℃ (corresponding to the working depth of 1 667 m), but it will suffer serious aging in the deep working temperature or the high temperature environment, which is the main reason for core burn and perforation failure in current applications. Hydrogenated nitrile rubber begins to age at a working temperature of 150 ℃ (corresponding to the working depth of 4 333 m), which is more stable than ordinary nitrile in mechanical properties, so it is reliable. Due to liquid column pressure and rubber aging, the maximum stress between the bushing and the rotor is decreases first and then increases with the increase of working depth. With the increase of the interference, the sealing performance of the PCP improves, and the maximum temperature of the sleeve section increases exponentially. For every 2 mm increase in the thickness of the rubber bushing, the true displacement of the inner wall increases by 0.059～0.067 mm on average, corresponding to the growth rate of 19%～28%. It is concluded that the working depth of 1 667 m is the boundary between the two types of rubber PCP. The interference is the minimum value of 0.5 mm, and the maximum wall thickness is 12 mm under the condition of no leakage. The research results provide theoretical support for reasonably matching the parameters of the stator rubber bushing, which optimizing the stator rubber material, and improving the working performance of the PCP throughout the life cycle.