This paper presents analytical results for the temperature and pressure fluctuations in a droplet or bubble pulsating in a sound wave, the related damping coefficients, as well as the corresponding sound attenuation coefficients for dilute suspensions. The study is limited to small-amplitude motions but includes the effects of compressibility and heat conduction in the fluid outside the particle. Results are obtained for both average and surface values of the particle's temperature and pressure fluctuations that are applicable to droplets in gases and liquids, and to gas bubbles in liquids. In the latter instance, it is found that the bubble's response exhibits a clear resonant peak at the isothermal natural frequency, that acoustic radiation is the dominant dissipation mechanism near resonance, and that the disturbances produced by the bubble in the liquid significantly reduce the thermal damping at most frequencies. Similar conclusions apply for droplets in liquids, except that the effects of resonance are significantly diminished.