Thermal errors are one of the major contributors towards positioning discrepancies in machine tools in precision machining. Along with friction and waste heat generated from production processes and internal heat sources, environmental influences around the machine tool create considerable thermal gradients followed by non-linear structural deformations. Efficient quantification of these three contributing sources of thermal errors are required in order to formulate a reliable thermal-error compensation system. The creation of all possible thermal configurations, which a machine tool could be subjected to, is experimentally infeasible and requires complex and time-consuming coupled flow and thermo-structural simulations. This paper presents a new approach in thermal error prediction by using CFD and finite element (FE) simulations to train a three-level interconnected neural network system. The first level essentially decouples flow simulations from thermo-structural simulations using optimal FE node points found using a Genetic Algorithm (GA), which significantly reduces the required training data. The boundary convection data obtained from this level is used in the second level to predict possible thermal configurations of the machine tool, after careful consideration of parameters related to internal heat sources and production processes. The third level maps these thermal configurations onto displacements on the machine tool.