Planck's data acquired during the first 15.4 months of observations towards both the disk and halo of the M31 galaxy are analyzed. We confirm the existence of a temperature asymmetry, previously detected by using the 7-year WMAP data, along the direction of the M31 rotation, therefore indicative of a Doppler-induced effect. The asymmetry extends up to about 10 degrees (about 130 kpc) from the M31 center. We also investigate the recent issue raised in Rubin and Loeb (2014) about the kinetic Sunyaev-Zeldovich effect from the diffuse hot gas in the Local Group, predicted to generate a hot spot of a few degrees size in the CMB maps in the direction of M31, where the free electron optical depth gets the maximum value. We also consider the issue whether in the opposite direction with respect to the M31 galaxy the same effect induces a minimum in temperature in the Planck's maps of the sky. We find that the Planck's data at 100 GHz show an effect even larger than that expected.