With her temp rising to 37.3 do you think in your experience that she ist ready yet? From her second mate she is day 63 tomorrow. She is just sleeping 24/7 lolFirst of all, no female of mine ever had her temperature fall below 36'7. What I HAVE experienced, however, is that the temp will go up and down. And once, when I thought for sure that we had reached the lowest of the low points, it turned out I was wrong, because the next day it went down even further and - importantly - STAYED THERE. Then the first-stage labor was unmistakable.
First stage labor should, in my experience, be starting now. Perhaps it has already begun without your being able to detect it. If you are in any doubt, then you will have to have the heart frequencies of the puppies checked by a vet who knows what he/she is doing. You say your vet does not know much about birthing. Don't you have an animal hospital somewhere in your area? They have to count the beats for at least one full minute (ultrasound) for
each individual puppy. (Do you know how many puppies are expected?) Don't quote me on it, but I believe the ideal frequency for an unborn puppy is 180 (beats per minute). From 140 downwards the puppy is in danger. If that should be the case, then a C-section might be in order.
Birthing is never without its trials, dangers and of course, joys and miracles! I do hope to hear that the signs of first-stage labor have become visible! With those temperature see-saws, something is definitely happening. I wish I knew your breed. It would be so helpful.