Eventually radiates out into space ;-) It doesn’t disappear, but we don’t need to care much about infrared passing Alpha Centauri.

Eventually yes, perhaps. But first heat gets trapped in Earth's atmosphere, because pollution and greenhouse gases make it hard for it to dissipate into space. It's called global warming, and no - it's not a hoax.

Except we have an lot of greenhouse gases that are really good at reflecting that infrared back down to earth.