Coming home tonight the gauge went slightly higher to just touching the warning light ( yes I know that's only a movement of about 1 or 2 mm, told you I was paranoid

Then when stopped ticking over went slightly higher to the middle of the warning light, which after about 5 to 10 mins the fan came on then I drove away and the needle dropped to just touching the warning light.
No water loss etc and drove fine.
It had a new pump , coolant and sensors about 4k ago.
Paranoid ?