Energy management in buildings is vital for reducing electricity costs and maximizing the comfort of occupants. Excess solar generation can be used by combining a battery storage system and a heating, ventilation, and air-conditioning (HVAC) system so that occupants feel comfortable. Despite several studies on the scheduling of appliances, batteries, and HVAC, comprehensive and time scalable approaches are required that integrate such predictive information as renewable generation and thermal comfort. In this paper, we propose an thermal-comfort aware online co-scheduling framework that incorporates optimal energy scheduling and a prediction model of PV generation and thermal comfort with the model predictive control (MPC) approach. We introduce a photovoltaic (PV) energy nowcasting and thermal-comfort-estimation model that provides useful information for optimization. The energy management problem is formulated as three coordinated optimization problems that cover fast and slow time-scales by considering predicted information. This approach reduces the time complexity without a significant negative impact on the result's global nature and its quality. Experimental results show that our proposed framework achieves optimal energy management that takes into account the trade-off between electricity expenses and thermal comfort. Our sensitivity analysis indicates that introducing a battery significantly improves the trade-off relationship.