I think if you're waking up at the same time in the morning, then your body will have made the same adjustments it does every day, so your temps would be accurate. It would be different if you temped at 2am one day, then 7am the next maybe, but if your body warms up every day, and you temp every day at that time, then why wouldn't it be accurate?
FWIW, when I temped the first time around, I took my temps at different times, though always around 6-8am, and I was always able to see a clear thermal shift. There were even mornings I forgot to temp before I got out of bed, and even then they were fine.