Heat flow and heat production measurements have been made in the vicinity of Long Valley from 0--30 km from the rim of the caldera and up to 30 km on either side of the boundary of the Basin and Range province at the eastern scarp of the Sierra Nevada. The search for a thermal anomaly assoicated with magma is complicated by the location of the caldera at the boundary between these two provinces with strongly contrasting regional heat flows and by unknown effects of hydrothermal circulation. The data show no conspicuous effect of the province transition possibly a small local heat flow anomaly near the east rim of the caldera, and a very substantial anomaly near the west rim. Simple heat conduction models suggest that Long Valley caldera is the surface expression of a deep magmatic system; an upper crustal magma chamber could not have sustained molten material throughout the 2-m.y. eruptive history unless it were resupplied with heat from deep crustal or subcrustal magmatic sources. If the heat were supplied by crustal intrusion of mantle basalt, the crust would thicken rapidly unless magmatic activity were accompanied by accelerated local crustal spreading. To generate a viable silicic magma chamber by sill injection in the upper 5--8 km of crust, minimum intrusion rates of the order of 1 m per century are probably required. Thermal models for the near-normal heat flow at the east rim suggest that magma beneath the eastern part of Long Valley caldera might have been exhausted during eruption of the Bishop Tuff 0.7 m.y. ago and that the resurgent dome, which subsequently formed in the west central caldera, marks the location of a residual chamber more circular in plan. High heat flow indicated by the single measurement near the west rim can be attributed to a simple shallow magma chamber beneath the western caldera or to recent local magmatism along the Sierra frontal fault system. Additional heat flow and hydrologic measurements are necessary for a confident interpretation of the thermal history and the present state of the caldera region.