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Nudging is a data assimilation technique that has proved to be capable ofreconstructing several highly turbulent flows from a set of partialspatiotemporal measurements. In this study we apply the nudging protocol on thetemperature field in a Rayleigh-B\'enard Convection system at varying levels ofturbulence. We assess the global, as well as scale by scale, success inreconstructing the flow and the transition to full synchronization whilevarying both the quantity and quality of the information provided by the sparsemeasurements either on the Eulerian or Lagrangian domain. We asses thestatistical reproduction of the dynamic behaviour of the system by studying thespectra of the nudged fields as well as the correct prediction of the heattransfer properties as measured by the Nusselt number. Further, we analyze theresults in terms of the complexity of the solutions at various Rayleigh numbersand discuss the more general problem of predicting all state variables of asystem given partial or full measurements of only one subset of the fields, inparticular temperature. This study sheds new light on the correlation betweenvelocity and temperature in thermally driven flows and on the possibility tocontrol them by acting on the temperature only.

Reconstructing Rayleigh-B\'enard flows out of temperature-only measurements using nudging