The thermal equilibrium of tokamak plasmas is studied by solving the electron and ion energy balance equations numerically. Three basic types of thermal equilibria, depending on different boundary temperatures, are found. The presence of a fold or cusp catastrophe structure of the equilibrium curves for temperature versus density in the case of low-boundary temperature indicates the existence of a density limit beyond which no equilibrium or only a trivial equilibrium exists. Major disruptions are considered to occur because of the loss of thermal equilibrium of the tokamak plasma. The study shows that major disruptions can be parametrically controlled. Thermal equilibria with higher boundary temperature display a monotonic structure of the temperature versus density curve, indicating good confinement characteristics and hence the absence of disruptions.