Such particles enter into Earth's atmosphere and burnt up generating light and heat. That is why you don't find photons in out space but a flare of them within the atmosphere. It also explains why earth cools rapidly on the shadow side. If we are within the hot zone, \(T\) should be in thermal equilibrium with Earth all around it, no matter which direction you are facing. \(T\) is like a fluid that flows around and engulf all inside the hot zone. Earth like a ball in water, there is no shadow side. The dynamics of Earth's spin and rotation however might affect the flow and ebb of the star dust and so effect temperature immediately.
But what is the nature of this star dust? If this is true. Hydrogen atoms? And so the sky is blue? Did Rayleigh scattering explained away everything?