In thermal solid freeform fabrication of layered products, simultaneous quality assurance of the part geometry and material structure requires concurrent design of the process conditions with the product features. For a heat transfer analysis yielding the material structure, an analytical, distributed-parameter quasi-linear thermal model is developed and tested in scan welding. This is based on Green’s field, identified in-process by infrared temperature sensing to reflect thermal nonlinearities. Similarly, a mass transfer model of the layer surface geometry is established on an analogous concept of the material deposition field, approximated by an ellipsoidal shape and identified in-process by Laser 3D scanning of the part topology in fused deposition modeling tests. The invertibility and computational efficiency of both models provide a basis for design of adaptive feedback control strategies for the thermogeometrical characteristics of rapid prototypes.