It's actually the coolant light which is blue. It's a rudimentary temp indicator. The blue is annoying but it should be on for several minutes while the engine is still below temp. No light means good. If it starts to get hot the same light will blink red, and if it's solid red that is well and truly overheated.
Would rather have a damn gauge myself.
This light should be hard to miss within the round center gauge. If you don't notice a blue coolant light when you first start the car, something may be wrong. Or you are mistaking it for the high beams, LOL. Or maybe you don't have one if you're not in the US, but I thought this was pretty universal now.
You should be gentler with any car while this light is on, or otherwise for the first several minutes. Until it gets to operating temp. If it's another car that has a gauge, you can use that as your, well, gauge.