Final answer:
A burning sensation in the premolar region caused by a mandibular denture is most likely due to pressure exerted on the lingual branch of the trigeminal nerve or the mental branch of the inferior alveolar nerve.
Step-by-step explanation:
If a complete mandibular denture causes a burning sensation in the premolar region, this is most likely due to the denture exerting pressure on the underlying nerve. Given the location of the discomfort, the lingual branch of the mandibular division of the trigeminal nerve or the mental branch of the inferior alveolar nerve could be implicated. The mental nerve emerges from the mental foramen, which is an opening located on each side of the anterior-lateral mandible and is responsible for supplying sensation to the chin and lower lip. Therefore, if a denture presses on this area, it can cause a burning sensation due to the pressure on the nerve.