During sessile droplet evaporation, studies with IR thermography and shadowgraphs have indicated temperature pulsations. We confirm those observations with microthermocouples, but microthermocouples also indicate temperature pulsations in the atmosphere of the droplet. The pressure in this atmosphere pulsated as well and was correlated with the temperature pulsations in the droplet. Also, we find that if a droplet evaporates into its own vapor, there are no temperature or pressure pulsations. The pulsations occur only if the droplet evaporates into an atmosphere with a component having a heat of solution with the droplet when it adsorbs absorbs. None of the currently proposed mechanisms for the temperature pulsations provide an explanation for the coupling between the temperature pulsations in the droplet and the vapor-phase pressure pulsations, and for the absence of the pulsations when the system is single-component. As a mechanism for the pulsations, we propose that when a droplet is exposed to an atmosphere containing a component that has a heat of solution with the droplet, energy will be released from adsorption absorption. This energy will cause pulsations in the evaporation flux, and these pulsations could cause the observed temperature and pressure pulsations. We examine this mechanism by showing that, if the measured temperature pulsations in a water droplet exposed to a methanol atmosphere are used as the input to a theory of evaporation kinetics (statistical rate theory), the pressure pulsations of the water vapor in the methanol atmosphere are predicted and agree with those measured with a quadrupole mass analyzer. When the inputs and outputs are reversed in the theory, we find that the temperature pulsations in the droplet are correctly predicted from the measured water vapor pulsations in the atmosphere.