Carbon nanotubes (CNTs) grown in a thin film have shown great potential as cathodes for the development several field emission devices. However, in modeling these important devices we face substantial challenges since the CNTs in a thin film undergo complex dynamics during field emission, which includes processes such as (1) evolution, (2) electromechanical interaction, (3) thermoelectric heating and (4) ballistic transport. These processes are coupled, nonlinear, and multiphysics in their nature. Therefore, they must be analyzed accurately from the stability and long-term performance view-point of the device. Fairly detailed physics-based models of CNTs considering some of these aspects have recently been reported by us. In this paper, we extend these models and focus on their computational implementation. All components of models are integrated at the computational level in a systematic manner in order to accurately calculate main characteristics such as the device current, which are particularly important for stable performance of CNT thin film cathodes in x-ray devices for precision biomedical instrumentation. The numerical simulations reported in this paper are able to reproduce several experimentally observed phenomena, which include fluctuating field emission current, deflected CNT tips and the heating process.