Experimental vibrational action spectra for the proton-bound dimer of dimethyl ether at different temperatures are compared with predictions based on AIMD computational simulations. Single photon spectra of argon-tagged ions in a low-temperature moleclar beam are found to agree well with the dipole-autocorrelation function (FT-DAC) from AIMD simulations of the system at 68K. Similarly good agreement is found between infrared multiple photon dissociation (IRMPD) spectra of room temperature ions in an ion trap and the FT-DAC from 270K AIMD simulations. As expected, the vibrational bands in the IRMPD spectra are much broader than the lower temperature argon-tagged spectrum. A detailed analysis of this broadening is presented in terms of the contributions of the normal modes of the molecule to the velocity autocorrelation function (FT-VAC) of each spectral band at high and low temperature. Ab initio calculations predict four harmonic normal modes, all involving significant motion of the bound proton, and these �light modes� contribute the vast majority of the intensity to the spectrum at all temperatures. At 68K, the vibrational bands are narrow and show close correspondence with the harmonic spectrum, although there is a splitting of the band near 1000 cm-1 into a doublet, due to coupling with a dark mode. This splitting precisely matches a similar doublet in the low-T argon-tagged spectrum. At 270K, the vibrational bands are broadened by coupling of many dark modes due to vibrational anharmonicities and the conformational flexibility of the ionic complex.