The heat-flow profile across the Arabian Shield from Ar Riyad to Ad Darb and across the Red Sea is examined for compatibility with the lithospheric structure of the area as deduced from geologic and other geophysical data. Broad continental uplift associated with Red Sea rifting is symmetric about the Red Sea axis, and geologic and geochronologic evidence indicate that uplift has occurred mainly in the interval 25-13 Ma (mega-annum) ago. Thermal-profile changes in the upper mantle resulting from an influx of hot material associated with rifting yield the correct order of magnitude of uplift, and this mechanism is suggested as the explanation for the regional doming. A lithospheric section, constructed from seismic refraction, gravity, and regional geologic data, provides the framework for construction of thermal models. Thermal gradient measurements were made in drill holes at five shot points. Geotherms for the Shield, which assume a radiogenic heat-source distribution that decreases exponentially with depth, yield temperatures of about 450?C at a depth of 40 km (base of the crust) for shot points 2 (Sabhah) and 3. The geotherm for shot point 4 (near Bishah) yields a distinctly higher temperature (about 580?C) for the same depth. Static models used to model the heat flow in the oceanic crust of the Red Sea shelf and coastal plain either yield too small a heat flow to match the observed heat flow or give lithosphere thicknesses that are so thin as to be improbable. Dynamic (solid-state accretion) models, which account for mantle flow at the base of the lithosphere, adequately match the observed heat-flow values. In the deep-water trough of the Red Sea, which is presently undergoing active sea-floor spreading, classical models of heat flow for a moving slab with accretion at the spreading center are adequate to explain the average heat-flow level. At shot point 5 (Ad Darb), the anomalous heat flow of 2 HFU (heat-flow units) can be explained in terms of a Shield component (0.8-1.0 HFU) and a component related to heating by the abutting oceanic crust a few kilometers away for periods exceeding 10 Ma. Analytical results are included for: 1) the cooling of a static sheet with an initial temperature distribution characteristic of a moving slab in a sea-floor spreading environment, and 2) the heating of a homogeneous quarter-space at its vertical boundary.