Power density of the Sun is approximately 276.5 W/m³. That’s counterintuitively little. A classic LED 3mm plastic package has the volume of less than 40 mm³ and some white ones can handle about 100 mW without a heatsink. Even leaving space for connections and airflow, you can easily overpower the Sun by volume by orders of magnitude.

A fun article mentioning that 276.5 W/m³ is about a reptile’s metabolism (and they famously produce little body heat): what-if.xkcd.com/148/

On replacing the Sun with another light source: what-if.xkcd.com/151/

Basically, as this Stack Exchange discussion correctly states, human intuition is quite useless when thinking about things orders of magnitude outside our experience.

Meanwhile, you say “hot” because that’s what your finger felt. Not really convincing of your ability to think in cosmic proportions.