Alternating current preheating (ACP) of lithium-ion batteries has the advantage of a high heating rate while inhibiting lithium plating. Two strategies based on terminal voltage control and full battery impedance control were proposed to simplify the ACP implementation. However, such strategies either severely compromise the preheating rate or induce non-negligible lithium plating. To maximize the preheating rate while ensuring no lithium plating, an ACP method based on anode potential control is developed using a square wave alternating current. The operation boundaries of lithium plating prevention, in terms of frequency and maximum permissible current amplitude, are determined using the anode potential and impedance. Their effectiveness in preventing lithium plating is validated by repeating 800 cycles of preheating. By applying the operation boundaries, a temperature-adaptive preheating is found to be able to speed up the preheating rate with higher frequency, smaller temperature intervals and better thermal insulation. When the battery is preheated at a frequency of 400 Hz, with a temperature interval of 5 °C and a heat transfer coefficient of 5 Wm⁻² K⁻¹, the preheating rate can reach 6.61 °C/min, exceeding the method based on the terminal voltage control by 5.4%, and larger than that based on the full battery impedance control strategy by 41.8%.