Remote Control Key Fails Intermittently

My remote control key on my 2011 535xi often fails when the car has been sitting in the sun. I have to manually unlock the car and hold the key to the steering column to start it. The temperature of the remote control doesn't seem to matter. The battery on the remote was putting out 3 V. I changed the battery to a new one (reading 3.1V) but it is the same. When the car cools off, the same remote works fine.

I took it to the dealer but it was working fine when I got there and they had no ideas.

Can anyone explain this to me?

thanks