If you have written in your thermal mapping protocol for autoclave as pressure is a criteria then i think yes, you may need to monitor that too.
If you have not specifically mentioned that, then i think temperature monitoring and recording will work.
I m asking this question for protocol and my question is that , Is there any International requirement to monitor the pressure during the sterilization
process for PQ of an Autoclave?
Steam push cleansing requires a compounding of pressure, broad temperatures, and moisture, and serves as one of the most widely used methods for cleansing where these functions will not effect a load. The simplest example of a steam push sterilizer is a home push cooker, though it is not recommended for accurate sterilization. Its important component is a room or vessel in which items for cleansing are sealed and subjected to broad temperatures for a specified length of time, known as a cycle.