We have developed a simple model to investigate the modifications of the hydrodynamics and nonequilibrium ionization X-ray emission in young supernova remnants due to nonlinear particle acceleration. In nonlinear, diffusive shock acceleration, the heating of the gas to X-ray-emitting temperatures is strongly coupled to the acceleration of cosmic-ray ions. If the acceleration is efficient and a significant fraction of the shock ram energy ends up in cosmic rays, compression ratios will be higher and the shocked temperature lower than test particle, Rankine-Hugoniot relations predict. We illustrate how particle acceleration impacts the interpretation of X-ray data using the X-ray spectra of Kepler's remnant, observed by ASCA and the Rossi X-Ray Timing Explorer. The thermal X-ray emission provides important constraints on the efficiency of particle acceleration, in complement to nonthermal emission. X-ray data from Chandra and XMM-Newton, plus radio observations, will be essential to quantify nonlinear effects.