We demonstrate that elastic scattering between dark matter (DM) and baryons can affect the thermal evolution of the intergalactic medium at early epochs and discuss the observational consequences. We show that, due to the interaction between DM and baryons, the baryon temperature is cooled after decoupling from the CMB temperature. We illustrate our findings by calculating the 21 cm power spectrum in coexistence with a velocity-dependent DM elastic scattering cross section. For instance, for a DM mass of 10 GeV, the 21 cm brightness temperature angular power spectrum can be suppressed by a factor of 2 within the currently allowed DM-baryon cross section bounded by the CMB and large-scale structure data. This scale-independent suppression of the angular power spectrum can be even larger for a smaller DM mass with a common cross section (for instance, as large as a factor of 10 for md∼1  GeV), and such an effect would be of great interest for probing the nature of DM in view of forthcoming cosmological surveys.