The consequences of an early epoch of plate tectonics on Mars followed by single-plate tectonics with stagnant lid mantle convection on both crust production and magnetic field generation have been studied with parameterized mantle convection models. Thermal history models with parameterized mantle convection, not being dynamo models, can provide necessary, but not sufficient, conditions for dynamo action. It is difficult to find early plate tectonics models that can reasonably explain crust formation, as is required by geological and geophysical observations, and allow an early magnetic field that is widely accepted as the cause for the observed magnetic anomalies. Dating of crust provinces and topography and gravity data suggest a crust production rate monotonically declining through the Noachian and Hesperian and a present-day crust thickness of more than 50 km. Plate tectonics cools the mantle and core efficiently, and the core may easily generate an early magnetic field. Given a sufficiently weak mantle rheology, plate tectonics can explain a field even if the core is not initially superheated with respect to the mantle. Because the crust production rate is proportional to temperature, however, an early efficient cooling will frustrate later crust production and therefore cannot explain, for example, the absence of prominent magnetic anomalies in the northern crustal province and the northern volcanic plains in the Early Hesperian. Voluminous crust formation following plate tectonics is possible if plate tectonics heat transfer is inefficient but then the crust growth rate has a late peak (about 2 Ga b.p.), which is not observed. These models also require a substantial initial superheating of the core to allow a dynamo. If one accepts the initial superheating, then, as we will show, a simple thermal evolution model with monotonic cooling of the planet due to stagnant lid mantle convection underneath a single plate throughout the evolution can better reconcile early crust formation and magnetic field generation.