I use a deluo Bluetooth GPS receiver, and I'm seeing a similar story.
I did not have this problem for the first year and a half of using my device, however I was forced to remove the battery (due to fears of explosion, as the battery was 'growing' in size.) If I try to use the GPS after the unit has been sitting in the sun all day long, it will simply refuse to send any NMEA messages across the bluetooth. When I let it cool off with a bit of air conditioning and turn it back on, it will eventually start sending messages. I didn't have this problem before when it operated with the battery in. I used to leave it turned on 24/7, and just let it's battery die out when I wasn't using it.
So, in the mean time, I'm also looking for a permanent solution for a bluetooth GPS unit that uses the SiRF chipset, something that's able to withstand the heat of a car that sits in the sun all day long!