If a Dyson sphere captures a large proportion of the radiation from a star, what is the destiny of that energy? It gets converted into other kinds of energy, a

If a Dyson sphere captures a large proportion of the radiation from a star, what is the destiny of that energy? It gets converted into other kinds of energy, and eventually becomes waste energy, ending up as low-grade heat. Hence the search for infra-red sources. But the amount of energy that a Dyson sphere absorbs must be equal to the amount of low-grade heat it radiates; so I'd expect a Dyson sphere to be very bright in infra-red - much brighter than brown or red dwarfs. Such an object should be quite easy to spot.