This paper is to study the practical critical current of No-insulation (NI) high temperature superconducting (HTS) coils under local heat disturbances. Based on a multi-physics model that built from an electric network model, a thermal coil model and a magnetic field model, behaviors of a HTS coil under different currents and heat disturbances are compared in this paper. A balance model of HTS coils with tiny persistent Joule heating is proposed, which is compared with the practical measurement results of a REBCO coil and shows a good agreement. In condition of persistent Joule heating, the practical critical current of the coil model is significantly less than the theoretical value. The work can provide an important reference to the analysis of HTS magnets quench behavior.