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In Norway, a large portion of the building stock originates from the period from 1955 to 1990. Many of these buildings fail to comply with the current building regulations regarding the energy consumption. In this study, the possibility for upgrading a hypothetical apartment building with an oil-based heating system has been investigated employing simulations from the IDA Indoor Climate and Energy software. For the construction of the original building, customs and regulations from the period 1981-90 were employed, and the building envelope was upgraded to the requirements of the Norwegian research centre on Zero Emission Buildings. Two alternative heating systems have been investigated: solar thermal collectors (i) alone and (ii) as combined with borehole thermal storage and a ground-source heat pump. For each case, the energy consumption, thermal comfort and indoor climate were studied. The simulations predict a reduction in the total annual heat demand to one third of the original with the upgrading. For the alternative heating systems, with solar collectors alone the demand for additional electric heating was still considerable, however in the combined system it was negligible. Regarding thermal comfort, in the upgraded building longer periods with elevated temperatures were observed.