A lumped-parameter, analytical model of material and thermal transfer is established in this paper for metal deposition by a moving, concentrated source. This is a dynamic description of the distinct width, height, length and temperature of the ellipsoidal molten puddle, expressed with respect to the torch power, material feed and angle, and the source motion. This is established through scalar mass, momentum and energy balances of the puddle control volume, and thermal conduction in the substrate. The model is validated by GMA Welding experiments, through measurements by an infrared camera and a Laser profilometry scanner. These sensors are next employed for real-time identification of the model efficiency parameters. Open-loop testing with parameter adaptation was conducted for the bead cross section profile during changes of the torch velocity, and the applicability of such geometry regulation to geometry control is discussed.