A new constellation of radio occultation satellites called COSMIC‐2 (Constellation Observing System for Meteorology, Ionosphere, and Climate‐2) is providing unprecedented dense measurements of the tropical atmosphere, with on average more than 4,000 high quality observations per day over 40°N–S. We use these data to evaluate large‐ and small‐scale thermal variability in the tropical lower stratosphere during October 2019 – April 2020. Space‐time spectral analysis of 6‐hourly gridded COSMIC‐2 data reveals a rich spectrum of traveling planetary‐scale waves, including Kelvin waves, mixed Rossby‐gravity waves and inertia gravity waves, in addition to propagating diurnal tides. These coherent modes show enhanced amplitudes from the tropical tropopause through the lower stratosphere (∼17–25 km). Characteristics of small‐scale temperature variances, calculated as deviations from the gridded fields, reveal systematic spatial patterns including time average maxima over Africa and South America overlying frequent deep convection. Small‐scale variances also exhibit transient maxima in the equatorial lower stratosphere tied to local variations in static stability, associated with large‐scale Kelvin waves. The new COSMIC‐2 observations provide novel details on the rich spectrum of large‐ and small‐scale waves near and above the tropical tropopause.