What is the issue with using interstellar dust to resolve Olbers’ Paradox?

The dust would eventually absorb so much energy that it would heat up and begin to glow just as brightly as the stars themselves

Early explanations suggested that intervening interstellar dust might obscure the light from very distant stars, thus darkening the sky. However, this explanation is physically unstable. If enough dust were present to effectively block the light emitted by all stars throughout the infinite volume, this dust would continuously absorb vast amounts of stellar radiation. This absorption process would cause the dust itself to reach a high thermal equilibrium, leading it to heat up significantly. Once heated sufficiently, the dust would begin to radiate energy and glow just as brightly as the stars it was meant to obscure, thereby failing to resolve the paradox and resulting in a bright sky regardless of the intervening material.