The original battery in my 2006 6S was replaced by the dealer in January 2014 (seven years for a battery in a new car is a record for me, in Iowa where it gets cold in the winter). After battery replacement, my temperature display would be blank when the key was in the On position before the engine started, and would either be blank or show the correct temperature in Fahrenheit after the engine was started. The car was returned to the dealer who stated they found no literature that said it was working incorrectly.
After searching this forum, I found a Mazda 3 post which suggested removing and cleaning a particular fuse connection in the internal fuse panel (located to the left of the driver's left foot) might address the problem. The particular fuse is a 15 Amp fuse labeled "ROOM" (the fuse labels are shown on the back side of the internal fuse panel door). I removed this fuse and cleaned the electrical connections of the fuse with electrical contact cleaner from Radio Shack then reinstalled the fuse. (I found a handy fuse puller in the fuse box in the engine compartment - it is made of white plastic and it is easy to find because of its color. Needle nose pliers can be used, but the fuse puller grips the fuse much more securely.)
After cleaning the fuse, my temperature display shows the temperature as soon as the key is turned to the On position, and it has worked correctly every time I have started the car after the fuse cleaning (about 10 times).
I did have to empty the 6 CD player of all discs before it would work correctly (it kept trying to empty a disk from a slot that was already empty, until I turned the engine off) since removing this fuse also removed power to the CD player. I had to reset the clock as well, since the clock is powered through the ROOM fuse.
It seems that the only effect of cleaning the fuse was to make a fresh, good connection to the temperature display. But so far, that seems to be enough.