Application of apatite (U-Th)/He thermochronology has been hindered by incomplete understanding of single-grain age dispersion often displayed by samples, particularly those from older, slowly cooled settings. To assess the capability of continuous ramped heating (CRH) to explain dispersion, we performed a study on an apatite suite from Cathedral Rocks in the Transantarctic Mountains (TAM) that have high age dispersion. Examining 132 apatite grains from a total of six samples, we confirmed earlier apatite (U-Th)/He results showing that measured AHe ages have at least three-fold intra-sample dispersion with no obvious relationships between ages and effective uranium concentration (eU) or grain size. CRH results on these apatites yielded two groups. Those with younger ages, characterized by single-peak incremental 4He gas-release curves, displayed simple volume diffusion behavior. In contrast, grains with older ages generally show anomalous gas release in the form of sharp spikes and / or extended gas-release at high temperatures (i.e., >= 800 °C). Well-behaved apatites still show considerable age dispersion that exceeds what grain size, radiation damage, and analytical uncertainty can explain, but this dispersion appears to be related to variations in 4He diffusion kinetics. The screened AHe ages from well-behaved younger apatite grains together with kinetic information from these grains suggest that the sampled region experienced slow cooling prior to rapid cooling (rock exhumation) beginning ca. 35 Ma. This interpretation is consistent with other studies indicative of an increase in exhumation rates at this time, possibly related to the initiation of glaciation at the Eocene-Oligocene climate transition. An attempt to correct anomalous older apatite ages by simply removing extraneous gas-release components is proposed yielded some ages that are too young for the samples’ geologic setting, suggesting that the factors that lead to anomalous laboratory release behavior can impact both the expected radiogenic component as well as those that are extraneous. From our observations we conclude that: (1) CRH analysis can serve as a routine screening tool for AHe dating and offers opportunities to reveal first-order kinetic variations; (2) model-dependent age correction may be possible but would require some means of estimating the broad proportions of 4He components incorporated into grains before and after closure to diffusion, and (3) interpretation of highly dispersed AHe ages requires assessment of individual-grain diffusion kinetics beyond that predicted by radiation-damage models. We also infer that many apatite grains contain imperfections of varying kinds that contribute significantly to kinetic variability beyond that associated with radiation damage.