Sounds like you have a dieing voltage regulator on your alternator.
When cold, it works fine, but once heated up the components wont function properly and it ceases charging your battery.
Roll on over to autozone or some store to get it tested for free. If your in europe, I'm not sure where to suggest that you go but I'm sure some place will test it for free without the need to remove the alternator from the car.
Get this fixed soon as this process (cycling it's charge very deeply) will RUIN your battery.