Even with 0.1°C precision, time of day makes an insanely huge difference.
Taking temp at the same part of your daily schedule, e.g., on awakening, will still show substantial variation based on just waking up earlier/later, or if something skews your sleep cycle -- and by substantial, I'm talking about >1.2°C.
Take temp at different times of day, and you're looking at >2°C normal variance between early morning low and mid-afternoon high.
Source: while training & competing at an international level, I took resting Temp/HR/BP readings 2x per day to regulate the training intensity schedule (unusual increases in resting values provided early warning for overtraining or illness, so could back off a smaller amount earlier rather than being forced to a larger rest later). What I found was that the temp numbers were extremely sensitive to the huge daily temp cycle, and that I had to constantly compensate reading that value.
It's really interesting, but unless you're very consistent and understand the daily cycle and variability, really hard to base anything on it (and I'm not even considering the F hormone cycle which is what they're apparently trying to measure).