Recently, no insulation (NI) and partial insulation (PI) techniques are proposed and studied for the compact and stable high temperature superconducting (HTS) coils. We have been studied the methods to improve the self-protection ability of HTS coils by removing the turn-to-turn insulation and inserting a metal tape instead of an electrical insulation. The operating current in the NI and/or PI HTS coils would be bypassed into the transverse direction by generated normal region in the HTS coils, and the method to control the current bypassing into the turn-to-turn direction in the NI HTS coil for controlling the effective number of turns was investigated previously. In this study, the characteristics of current bypassing and transient stability in PI HTS coils were studied experimentally. The 20 turns single-pancake PI HTS coils wound with GdBCO coated conductor with/without the stabilizer and co-winding PI HTS coil with Cu tape were prepared and tested experimentally. The thermal properties and current bypassing characteristics due to the normal region created by heaters (Strain gauge) were studied as functions of the number of heater, position of heater, amount of input heating and shape of PI at liquid nitrogen temperature and background magnetic field of 0.6 T. The experimental results including optimized shape of PI and positions of heater to control the current bypassing will be presented.