The X-ray and $\gamma $-ray burst signatures of Thermonuclear Supernovae are studied. We identify two potential mechanisms: The breakout of the thermonuclear burning front, and the interaction of the rapidly expanding envelope with material within (!) the progenitor system. Our study is based on the delayed detonation scenario because this can account for the majority of light curves, spectra and statistical properites of 'Branch-normal' SNe~Ia. Based on detailed radiation-hydro calculation which include nuclear networks, we find, for both mechanisms, peak luminosities of the order of $10^{50} erg/sec $ and fringe-like light curves with time scales of a few tenth and a few seconds, respectivly. Whereas the breakout will produce radiation mainly in the X- and soft-$\gamma $ ray range, typical energies in the second case are higher by an order of magnitude. In general, we expect a fast rise and slow decline and, after the peak, an evolution fromhard to softer radiation due to adiabatic expansion. We discuss the detection (or limits) of X- and $\gamma $-rays for SNe~Ia as diagnosticaltools to decipher the explosion physics and the nature of the progenitor system. We present a statistical analysis of historic GRB data and the correlation with known SNe~Ia. The results are suggestive that SNe~Ia may contribute to the population of short X-ray and GRBs.