The application of adaptive control for a class of multivariable processes in heating, ventilating and air conditioning (HVAC) systems is studied. As an example, a two zone fan-coil heating (FCH) system is considered. The thermal dynamics of the FCH system and environmental zones are simulated by a nonlinear model. The environmental zones are acted upon by multiple disturbances, such as changes in outdoor temperature, solar radiation fluxes and dynamic disturbances due to the thermal inertia of the enclosure elements. The control objective is to hold the zone temperatures and the boiler temperature close to their respective setpoints irrespective of the changes in disturbances acting on the system. A multivariable adaptive controller based on LQR (Linear Quadratic Regulator) theory is designed. Simulation results showing the closed loop response of the system to changes in operating points, external disturbances, changes in system parameters and unmodeled dynamics are presented. It is shown that the adaptive controller is able to adapt to a wide range of operating conditions and is able to maintain the zone temperatures and the boiler temperature close to their respective setpoints.