Energy flexibility is a cost-effective solution to facilitate secure operation of the energy system while integrating large share of renewables. Thermal energy infrastructure is a great asset for flexibility in systems with widely developed district heating networks. The aim of the present work is to investigate the potential for low-energy residential buildings to be operated flexibly, according to the needs of district heating system. An apartment block is studied, utilizing the storage capacity of thermal mass as storage medium. Two sets of data are utilized: heat load of Greater Copenhagen and dynamic heat production cost which is used as a price signal for the scheduling of the heating use in the building. Scenarios with different control signals are determined in order to achieve load shifting. The findings show that pre-heating is highly effective for load shifting and peak load reduction. During morning peak load hours, energy use is reduced in all scenarios between 40% and 87%. Although with load shifting higher energy use may occur, it occurs mostly at times when the city heat load is lower and heat production is less expensive and less carbon-intensive. Indoor temperature has a wider range and/or more fluctuations, yet remains within acceptable limits.