In this paper the transformation-circle diagrammatic approach is developed. Using this method, the general solution of the thermal-insensitive resonator is derived, that is, the σ1 circle is tangential to the πf circle. Its main characters arc elucidated clearly. Some inaccurate current points of view on its characters are made clear. Furthermore, the special solution of the optimal thermal-insensitive resonator is obtained, that is, g1*g2*=1/2; L2= 0 or L2=R2.