Yaris 2007 Battery and Diesel filter warning lights in cold weather

[Dallaz]

Hi, first post here :)

I bought a used Yaris 2007 D4D some months ago, and I have noticed a strange issue. When the temprature goes below about 5 negative celsius (23 F) the battery and diesel filter warning lights both flicker and/or stay on almost fully lit for about 15-20 minutes before they both go away.

I read on the forum that someone suggested to check a fuse in the engine room if the battery light is flickering, but I haven't managed to find that one (even if i looked around in there with a torch). I also read that there might be a problem with the alternator...

Some observations:
- Doesn't seem to have something to do with engine being cold or not.
- The two lights are only showing at the same time, not just one of them.
- Battery seems just fine
- in warmer weather the two warning lights flicker for some seconds about 30 seconds after the car is started and then go away.

I have been thinking about ordering a used alternator online and get the local mecanic to replace it since I'm not that used to working on cars myself... But right now I don't really know if the alternator is the culprit.

Any suggestions?