Thermal pain arising from the teeth is unlike that arising from anywhere else in the body. The source of this peculiarity is a long-standing mystery that has begun to unravel with recent experimental measurements and, somewhat surprisingly, new thermomechanical models. Pain from excessive heating and cooling is typically sensed throughout the body through the action of specific, heat sensitive ion channels that reside on sensory neurons known as nociceptors. These ion channels are found on tooth nociceptors, but only in teeth does the pain of heating differ starkly from the pain of cooling, with cold stimuli producing more rapid and sharper pain. Here, we review the range of hypotheses and models for these phenomena, and focus on what is emerging as the most promising hypothesis: pain transduced by fluid flowing through the hierarchical structure of teeth. We summarize experimental evidence, and critically review the range of heat transfer, solid mechanics, fluid dynamics, and electrophysiological models that have been combined to support this hypothesis. While the results reviewed here are specific to teeth, this class of coupled thermomechanical and neurophysiological models has potential for informing design of a broad range of thermal therapies and understanding of a range of biophysical phenomena.