Several Thoughts (Although it has been awhile since I have done Autoclave work).
There needs to be a clear interpretation as to what is meant by a cold spot. By definition there will ALWAYS be a cold spot. The question is does it reside within an acceptable temperature distribution? There is a huge difference between having a cold spot of 121.4 C and one of 117.4 C.
Furthermore is this a distribution cold spot or a penetration cold spot?
The distribution cold spot is a OQ based activity in my opinion and is reflective of the performance of that machine. I know most publications/standards/guidances such as PDA/USP/EN give a proper range of temperatures in the Empty Chamber.
If its not something that a repair fixes and is truly reflective of the capability of the machine then the question needs to be asked how well was the build of the machine controlled from a specification standpoint.
Certainly if this is a a legacy equipment then it needs to be considered if it’s fit for purpose and what procedural controls are in place for this machine. Furthermore you will have an uphill battle with regulators to say why you chose to ignore guidance documents.
On the penetration side there can be cold spots but that is a different scenario. Quantitative data such as FO and BI results can be used to determine truly if you are acheiving appropriate SALs. Beware of the European Regulation (not sure if it still exists) where they look for Penetration Uniformity within a quick amount of time during exposure.
Lastly Following what has been previously identified is your approach a bioburden based one or is it an overkill approach? Certainly you require precise control for a bioburden approach.