The relationship between Type Ia supernovae and the thermal X-ray emission from their young supernova remnants is explored using one dimensional hydrodynamics and self- consistent ionization and electron heating calculations coupled to a spectral code. The interaction with the ambient medium is simulated for a grid of supernova explosion models which includes all the physical mechanisms currently under debate. The differences in density profile and chemical composition of the ejecta for each supernova explosion model have a profound impact on the hydrodynamic evolution, plasma ionization and emitted thermal X-ray spectra of the supernova remnant, even several thousand years after the explosion. This has two important consequences. First, new possibilities are opened for the use of the high quality X-ray observations of Type Ia supernova remnants as a tool to study supernova explosions. Second, it follows immediately that an accurate analysis of such observations is not possible unless the characteristics of the supernova explosion are considered in some detail. These results are applied to the remnant of the Tycho supernova (SN1572), which appears to be the result of a delayed detonation explosion based on a comparison between its X-ray spectrum and the synthetic model spectra. The imprint of the presupernova evolution predicted by current Type Ia progenitor models on the dynamics of the supernova remnants is also explored, and found to be important. The observations, however, do not show hints of any such imprint.