Several demand response (DR) strategies rely on real-time pricing and selfish local optimization, which may not result in optimal electricity consumption patterns from the viewpoint of an energy supplier or a power system. Thus, this paper proposes a strategy enabling centralized adjustments to cost-minimize consumers' load. By employing the strategy, an aggregator is able to alter electricity consumption in order to remove power imbalances and to participate in the balancing power market (BPM). In this paper, we focus on direct electric space heating (DESH) loads that aim to minimize their heating cost locally. The consumers and an aggregator agree about an indoor temperature band, within which the aggregator is allowed to alter the temperature, and thus the electricity consumption. Centrally, the aggregator procures its electricity demand from a day-ahead (DA) market by utilizing the allowed temperature band and employs the band later in real-time (RT) operation for the balancing of its own imbalances or regulating power in the BPM.