Cosmic microwave background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a linearized formula for relating them to the temperature blackbody fluctuations. However, this procedure also generates a signal in the maps in the form of y -type distortions which is degenerate with the thermal Sunyaev Zel'dovich (tSZ) effect. These are small effects that arise at second order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of our peculiar velocity, the tSZ and primordial y -distortions. They can nevertheless be well modeled and accounted for. We show that the distortions arise from a leakage of the CMB dipole into the y -channel which couples to all multipoles, mostly affecting the range ℓ ≲ 400 . This should be visible in Planck's y -maps with an estimated signal-to-noise ratio of about 12. We note however that such frequency-dependent terms carry no new information on the nature of the CMB dipole. This implies that the real significance of Planck's Doppler coupling measurements is actually lower than reported by the collaboration. Finally, we quantify the level of contamination in tSZ and primordial y -type distortions and show that it is above the sensitivity of proposed next-generation CMB experiments.