We study temperature propagations and convective instabilities induced in critical fluids experimentally, theoretically and numerically. The analytical system is as follows: A critical fluid, the temperature of which is slightly higher than the critical temperature, is confined between two horizontal plates. The temperature of the bottom plate is raised at time zero and the temperature of the top plate is kept at the initial temperature of the fluid. An experimental system for the visualisation of convection induced in critical C02 is developed. In the theoretical analysis, we derive the thermofluiddynamics equations of critical fluids, in which the compressibility of the fluids and the pressure dependence of the entropy are taken into account. We solve the governing equations by the control volume finite difference method, in which the MacCormack scheme is employed for the time derivative, and investigate the temperature propagation modes on short, intermediate and long time scales. Through the analysis, the following results have been obtained; (1) On short time scales: Temperature propagates very quickly as acoustic waves because of the high compressibility of the critical fluids. (2) On intermediate time scales: The system temperature rises quickly and becomes constant in the central part of the fluid because of the quick temperature wave propagations. Thin thermal boundary layers are established near the bottom and top walls although the top wall is not cooled. (3) Long time scales: Thermal plumes are induced upwards from the bottom thermal boundary layer. Plumes are also initiated downwards from the top thermal boundary layer although the top wall temperature is not cooled. The convective mode of the thermal plumes driven in the critical fluids are different from that of Rayleigh-Benard convection.