If the auditor is calling out the software specifically, perhaps you need to write into the SOP that the software used to monitor temps is kept updated (firmware updates and whatnot I guess?). If you're using an online portal for the monitoring through the company that owns it, asking them about maintenance to the portal could be something you keep filed to show they're handling such maintenance on their own.
This reminds me of a customer audit I had at a dry steam sterilization plant: they sent two gals to audit our tiny operation who seemed more excited to be partying in our city vs auditing us, but they came from a medical auditing background. They had a lot of objections we had to cover being a basic sterilization operation, but we ran into trouble with them when we told them time and temp is our preventative control for the log reduction in treated goods. They asked me to prove the clock that times our treatments was validated, and it legitimately was one of the first times in an audit for that company that I was dumbfounded...
"How do you know the program ran the treatment for 20 minutes at this temperature?"
"Um....Because the computer says so?"
"How do you verify the time recorded by the computer is accurate?"
*me and the CEO nervously shrugging at each other*
"Because it's a windows machine and Bill Gates says the clock works.....?"
They dropped it after that because we showed we purposely overrun the times specified in our validation studies by a fair margin, but asking me how I validate the clock on a desktop computer is accurate seemed like something that really applies to the medical field vs that small outfit I used to be with lol.