The cosmic microwave background appears hotter in Earth’s direction of motion because of the Doppler effect. As Earth and the Solar System move toward incoming CMB photons, their waves are compressed, increasing their observed frequency and energy. In the opposite direction, the waves are stretched and appear slightly cooler.
The CMB is relic radiation released when the early universe became transparent, roughly 380,000 years after the Big Bang. Today it has an almost perfect blackbody temperature of about 2.725 K, but motion creates a small temperature dipole across the sky.
This effect is not the same as the CMB’s cosmological redshift. Cosmic expansion stretched the radiation over billions of years, cooling it from its much hotter origin; the Doppler effect describes the additional shift caused by the observer’s motion relative to the CMB’s rest frame. Measurements of this dipole show that the Solar System moves at about 370 km/s relative to that frame.