Studies on propagation of high amplitude N-waves in turbulent atmosphere are relevant to the sonic boom problem which involves high interest due to development of new civil supersonic aircrafts. In this problem it is important to predict the effect of turbulence on the statistical characteristics of random variations of the wave amplitude and shock rise time. In the present work, in relation to the sonic boom problem, the propagation of high amplitude spark-generated N-waves through a layer of thermal turbulence was studied in a model laboratory-scale experiment which is more controlled and reproducible than field measurements. Evolution of statistical distributions of the wave amplitude and shock rise time was investigated at different propagation distances from the spark source. The results were compared to experimental data known from the literature, where N-waves were propagated through a kinematic turbulence. It was shown that for similar propagation distances, turbulent length scales, and index fluctuations in both experiments, kinematic turbulence leads to stronger distortion of the N-wave field. Moreover, with kinematic turbulence the probability to observe intense focusing at caustics is to 2 or 3 times greater than with thermal turbulence.