Structure and variability of temperatures in the tropical upper troposphere and lower stratosphere (~10--30 km) are studied based on Global Positioning System Meteorology (GPS/MET) observations during April 1995 to February 1997. Comparisons with several hundred colocated radiosondes demonstrates the high accuracy of GPS/MET retrievals in the tropics. Mean structure and variability of the tropical cold point tropopause is examined, and much of the subseasonal variability in cold point temperature and height appears to be related to wave-like fluctuations (such as gravity waves or Kelvin waves). Significant correlations are found between the GPS/MET temperatures and daily, gridded outgoing longwave radiation data (a proxy for tropical deep convection), providing independent confirmation of the GPS/MET temperature fluctuations. These correlations quantify the large-scale tropical temperature response to transient convection, showing coherent wave-like variations over ~12--18 km which span a hemisphere in longitude. The GPS/MET data also show clear evidence of the stratospheric quasi-biennial oscillation (QBO) in temperatures over altitudes ~16--40 km.