A food heating appliance is disclosed that comprises a chamber portion and a lid portion that defines a heating chamber. The chamber portion has a perimeter wall extending about the heating chamber and an upper opening into the heating chamber. The perimeter wall is insulated to permit walls are A heating apparatus in the heating chamber comprises a heating element positioned in the heating chamber adjacent to the perimeter wall, and a shield positioned above the heating element to block debris from falling on the heating element. The shield may be sloped downwardly from the perimeter wall toward a center of the heating chamber. A holding tray for smoking material may be positioned adjacent to the heating element. A drip collection tray may be positioned at the bottom of the heating chamber that influences air flow into the heating chamber. Temperature control circuitry provides precise, predictive heating of the food.