Temperature fields in the equatorial upper troposphere and lower stratosphere, derived from GPS radio occultation measurements for 2001--2002, show evidence for planetary-scale Kelvin waves. These waves have a characteristic eastward phase tilt with height and typical vertical wavelengths of ~4--8 km. The Kelvin waves exhibit coherent vertical structure over ~12--25 km, with maximum amplitudes near the tropical tropopause (~17 km). The waves are often quasi-stationary near the tropopause but exhibit regular eastward propagation in the lower stratosphere (with periods near 20 days). The quasi-stationary waves modulate the climatological cold tropopause over Indonesia. The transient lower stratospheric waves show enhanced amplitudes coincident with the descending westerly shear phase of the quasi-biennial oscillation (QBO). Correlations with outgoing long-wave radiation (OLR) data show that global temperature patterns over ~12--17 km (with characteristic Kelvin wave structure) vary coherently with transient deep convection over Indonesia.