With growing interest in interoceptive training to enhance the perception of internal bodily signals, there is a need to consider the mechanisms by which training may improve performance on tests of interoceptive accuracy (i.e., tests designed to measure how well signals from the body can be perceived). In this brief paper we use the example of cardiac interoceptive accuracy training to outline several possible mechanisms by which such training may result in improvement on tests of cardiac interoceptive accuracy. We show that under many of these mechanisms, evidence of improvement on tasks that claim to measure cardiac interoceptive accuracy does not reflect improvement in the perception of cardiac signals. We provide several recommendations to mitigate the potential influence of factors unrelated to interoceptive accuracy, enabling it to be determined that an improvement in interoceptive accuracy has occurred following training.