Following recent studies evidencing the effect of deep overshooting convection on the chemical composition of the tropical lower stratosphere by injection of tropospheric air across the cold-point tropopause we explore its impact on the thermal structure of the tropical tropopause layer (TTL) and the lower stratosphere using the high-resolution COSMIC GPS radio-occultation temperature measurements spanning from 2006 through 2011. The temperature of the lower tropical stratosphere is shown to display a systematic mean cooling of 0.6 K up to 20 km in the late afternoon in the summer over land compared to oceanic areas where little or no diurnal variation is observed. The temperature cycle is fully consistent with the diurnal cycle and geographical location of deep convective systems reported by the Tropical Rainfall Measurement Mission (TRMM) precipitation radar suggesting strong injection of adiabatically cooled air into the lower tropical stratosphere in the afternoon over tropical continents. But most unexpected is the difference between the southern and Northern Hemispheres, the first displaying systematic larger cooling suggesting more intense convection in the southern than in the northern tropics.