I think many of you are missing the point of the posters question.
Is it REQUIRED to record something that is for food quality not food safety.
The answer is dependent on only a couple things:
Is it part of your food safety standard (SQF level 3)?: If no continue to next question. If yes: Record it.
Is it required by your customers or a regulatory body? If no continue to next question: If yes: Record it.
Do you care to know the temperature at all times?: If no then don't record it. If yes than do it.
That's the entire answer boiled down.
You don't HAVE to record something that is only product quality related unless you are applying for SQF level 3 or if you want to make sure your product is a quality product. If you will accept that some of your product may not be high quality during distribution than by all means don't record it. Nobody is going to make you.