Thermally activated buildings (TABs) have significant energy-saving and carbon emission reduction potential by integrating heat sources within the envelope and dynamically adapting to environmental changes. The heat source types and their operation strategies greatly affect the overall building thermal performance, which requires further evaluation and optimization. This study first developed an integrated simulation framework for TABs composed of a building energy model, a thermally activated envelope (TAE) physical model, and a heat source operation model. Both the low-grade thermally activated envelope (LTAE), which utilizes natural energy, and the high-grade thermally activated envelope (HTAE), which uses commercial heat sources, were investigated. The building indoor thermal comfort hour for LTAEs and annual heating and cooling energy consumption for HTAEs under different heat source operation strategies were evaluated through a low-carbon demonstration residential building for case study. For LTAEs, a dynamic on/off control strategy that considers indoor air temperature, supply water temperature, and TAE heat source layer temperature, increased the building's annual thermal comfort hour by over 72 % compared to a conventional building without TAEs. Similarly, for HTAEs, a dynamic strategy adjusting the supply water temperature inversely with outdoor air temperature reduced annual heating and cooling energy consumption, and operational carbon emissions by 42.52 %, 55.82 %, and 42.93 %, respectively, compared to a conventional building with SACs. The hybrid LTAE-HTAE approach further reduced heating energy consumption by 48.92 %, cooling energy consumption by 70.31 %, and operational carbon emissions by 51.16 %. This study provides scientific and effective guidance for the detailed design and operation of TABs.