No-insulation (NI) high-temperature superconducting (HTS) coils exhibit high thermal stability and self-protecting features compared with traditional insulated HTS coils. As NI coils experience heat disturbance, the underlying mechanism of the heat propagation, the changes of the central field and voltage of the coil need to be further explored. Moreover, due to the rapid temperature rise caused by the heat disturbance, the coil typically suffers from large strain and stress. Therefore, the mechanical behavior is also a vital factor in the design and operation of superconducting magnets. This paper proposes a multiphysics quench model to study the thermal stability, composed of an equivalent circuit axisymmetric model combined with a two-dimensional magnetic field model and a one-dimensional (1D) heat transfer model. An additional 1D solid mechanical model is used to analyze the mechanical behavior of the NI coil. The results indicate that when the temperature of the coil exceeds its critical value, the current flows along the radial direction. The heat generated by the radial resistance of the coil is small, so that it is difficult to induce a quench. The thermal expansion and heat propagation velocity also affect the distributions of the hoop and radial stresses in the coil. The change of the hoop stress is larger than that of the radial stress, and the electromagnetic force has a relatively small effect in the self-field. The pulsed energy, inner diameter of the coil and location of the heater are all found to have an observable effect on the thermal stability and mechanical behavior.