Battery light / temp gauge

My battery light came on last night and now stays on whenever the car is running. It flickered on yesterday afternoon after going through a big puddle.

This morning my temperature gauge is running pretty high, though my water levels are fine. The car doesn't feel like it's running hot and when I checked my water the engine didn't seem to be that hot (it had only been running for 10 or 15 minutes).

Is it coincidence?

I have read on here that it could be a case of my alternator being jiggered and needing replaced, or it could just be a wire. The battery charge is normal. I'm a bit confused that the temp gauge is racing as well.

Could be the wire has fallen off (as mine did on Friday night) or it's goosed, it happened when you went through water so it's possible.

Fix the alt and see if the temp issue goes away, it might, dodgy volages can screw with guages so see what happens.

DM