Thellier-type experiments are the most widely applied approaches for determining the absolute paleointensities of Earth's magnetic field. One major problem, however, is that specimens are prone to thermal alteration due to the intensive thermal treatment during experiments. Linear Arai plots with acceptable partial thermal remanent magnetization (pTRM) checks have been considered as evidence for the absence of or negligible effects of thermal alteration and as reliable indicators of high-quality paleointensity estimates. However, by simulating the Coe variant of the Thellier method on assemblages of single domain (SD) magnetite particles, it is demonstrated that new magnetic minerals, which form during thermal treatments, can result in linear, concave-up, or concave-down Arai plots depending on the magnetic properties of both the primary and secondary magnetic phases. Among this range of behavior, pseudo-ideal Arai plots, which are linear with acceptable pTRM check statistics, would lead to paleointensity underestimates. It is further demonstrated that pTRM checks are proportional to the degree of underestimate with a magnetic granulometry dependency for SD particles. Due to the complexity of this dependency, pTRM check statistics are only comparable when specimens have similar magnetic properties. This suggests that a universal threshold for pTRM check statistics is not likely to be effective. Since the criteria of linearity and low pTRM check statistics are insufficient to guarantee the fidelity of the estimates auxiliary rock magnetic methods such as temperature dependent hysteresis parameters and anhysteretic remanent magnetization are highly recommended to identify the presence of alteration.