The Columbia River flood basalts include some of the world's largest individual lava flows, most of which were fed by the Chief Joseph dike swarm. The majority of dikes are chilled against their wall rock; however, rare dikes caused their wall rock to undergo partial melting. These partial melt zones record the thermal history of magma flow and cooling in the dike and, consequently, the emplacement history of the flow it fed. Here, we examine two-dimensional thermal models of basalt injection, flow, and cooling in a 10-m-thick dike constrained by the field example of the Maxwell Lake dike, a likely feeder to the large-volume Wapshilla Ridge unit of the Grande Ronde Basalt. Two types of models were developed: static conduction simulations and advective transport simulations. Static conduction simulation results confirm that instantaneous injection and stagnation of a single dike did not produce wall rock melt. Repeated injection generated wall rock melt zones comparable to those observed, yet the regular texture across the dike and its wall rock is inconsistent with repeated brittle injection. Instead, advective flow in the dike for 3--4 years best reproduced the field example. Using this result, we estimate that maximum eruption rates for Wapshilla Ridge flows ranged from 3 to 5 km3 d-1. Local eruption rates were likely lower (minimum 0.1--0.8 km3 d-1), as advective modeling results suggest that other fissure segments as yet unidentified fed the same flow. Consequently, the Maxwell Lake dike probably represents an upper crustal (~2 km) exposure of a long-lived point source within the Columbia River flood basalts.