Dating lime mortar samples using the radiocarbon (14C) method can be difficult. This is because the contamination is similar to the primary dating material (CaCO3) and consequently difficult to remove. Mortar can also have late-in-formation pyrogenic carbonate from interactions with the environment after the initial hardening phase, such as recrystallization, fire damage or delayed hardening. When 14C dating a system of primary dating material, contamination and late-in-formation pyrogenic carbonate, one approach is multi-fraction dating with conclusiveness criteria. If a sample has sufficient contamination or late-in-formation pyrogenic carbonate, the criteria evaluate the result inconclusive. To improve inconclusive results from such samples, this study investigates sample preparation by thermal decomposition. Here samples that were inconclusively dated by the authors' traditional method, sequential dissolution with 85% phosphoric acid, are investigated further. This study finds that CO2 thermally decomposed at low temperatures contains some late-in-formation pyrogenic carbonate. By rejecting CO2 decomposed at low temperatures, Kastelholm castle and Kimito church in Finland are conclusively and accurately dated. Furthermore, a preheating method removes some late-in-formation carbonate, but not enough for a conclusive result. Finally, thermal decomposition finds difficulty in discerning binder carbonate from limestone and marble contamination.