Smart grid is one of the main applications of the Internet of Things (IoT) paradigm. Within this context, this paper addresses the efficient energy consumption management of heating, ventilation, and air conditioning (HVAC) systems in smart grids with variable energy price. To that end, first, we propose an energy scheduling method that minimizes the energy consumption cost for a particular time interval, taking into account the energy price and a set of comfort constraints, that is, a range of temperatures according to user's preferences for a given room. Then, we propose an energy scheduler where the user may select to relax the temperature constraints to save more energy. Moreover, thanks to the IoT paradigm, the user may interact remotely with the HVAC control system. In particular, the user may decide remotely the temperature of comfort, while the temperature and energy consumption information is sent through Internet and displayed at the end user's device. The proposed algorithms have been implemented in a real testbed, highlighting the potential gains that can be achieved in terms of both energy and cost.