Due to the high upper critical field and transition temperature, REBCO coated conductor show great promise for conduction-cooled magnet applications. The normal zone of high temperature conductor (HTS) spreads slowly, and the conversion of a weak spot into a hot spot is localized and quite fast. Hence, in-field critical current weak spot evaluation under the nonuniform temperature gradient is important for conduction-cooled magnet stability estimation. Cooling path design needs to take the weak spot into account. In this study, a temperature-field-angle dependent critical current estimation neural network was first trained based on a public database of HTS critical current. The equivalent thermal conductivity was applied for the interface contact between the turns. Thermal contact conditions were given to the interface between the coil and bobbin considering actual production situations, such as thermal grease. Combing the non-uniform magnetic field and thermal distribution, the critical current distribution was evaluated to track the weak part. The results of this study will be employed in the design analysis of high magnetic field conduction cooling magnets in the future.