Convective Quasi-Equilibrium (CQE) is often adopted as a useful closure assumption to summarize the effects of unresolved convection on large-scale thermodynamics, while existing efforts to observationally validate CQE largely rely on specific spatial domains or sites rather than the source of CQE constraints—deep convection. This study employs a Lagrangian framework to investigate leading temperature perturbation patterns near deep convection, of which the centers are located by use of an ensemble of satellite measurements. Temperature perturbations near deep convection with high peak precipitation are rapidly adjusted towards the CQE structure within the two hours centered on peak precipitation. The top 1% precipitating deep convection constrains the neighboring free-tropospheric leading perturbations up to 8 degrees. Notable CQE validity beyond a 1-degree radius is observed when peak precipitation exceeds the 95th percentile. These findings suggest that only a small fraction of deep convection with extreme precipitation shapes tropical free-tropospheric temperature patterns dominantly.