Horizontal path temperature fluctuation measurements were made on board a KC-135 aircraft, at altitudes ranging from 30,000 to 40,000 feet, such that the altitudes below, in, and above the tropopause were sampled. In general, we find that there is a low background level of turbulence, and there appear to be superimposed o this background higher level turbulent 'patches.' These patches are a few km in extent, and the boundaries of these patches are abrupt with the transition to background taking place in distances of approximately 50 meters. These abrupt boundaries are consistent with the optical measurements taken at the same time. The measured structure functions of the form D(r) is approximate to rn with 0.2<=n<=2 down to scale sized of 20 cm, which was the limiting resolution of the instrumentation. Each flight segment was conducted under constant conditions (i.e., speed, temperature, altitude). Contrary to expectations, the log slopes of either the power spectral densities or of the structure functions are often non-Kolmogorov, as characterized by a k-5/3 power spectral density, or by a structure function of the form r2/3. This statement must be tempered, however, by uncertainties in the frequency response of the temperature sensor. In addition, the data show regions in which the expected functional relation between the structure function and power spectral density does not hold. These characteristics of high-altitude turbulence suggest that past measurement techniques used to measure cn2 may be inapplicable in the high-altitude regime, and cn2 as a sole descriptor of turbulence may be incomplete.