Planck data acquired during the first 15.4 months of observations toward both the disk and halo of the M 31 galaxy were analyzed. We confirm the temperature asymmetry that was previously detected by using the seven-year WMAP data in the direction of the rotation of M 31, which indicates that this is a Doppler-induced effect. The asymmetry extends to about 10• ( 130 kpc) from the center of M 31. We also investigated the recent problem raised in Rubin and Loeb (2014, JCAP, 01, 051) about the kinetic Sunyaev-Zel'dovich effect from the diffuse hot gas in the Local Group, which is predicted to generate a hot spot of a few degrees in size in the cosmic microwave background maps in the direction of M 31, where the free electron optical depth is highest. We also considered whether the same effect in the opposite direction with respect to the M 31 galaxy induces a minimum in temperature in the Planck maps of the sky. We find that the Planck data at 100 GHz show an even stronger effect than that expected.