In order to promote the application of heat pump drying technology, a multifunctional heat pump drying device with heating was designed. The conventional drying, constant temperature drying, and various operating modes were refrigerated, and the corresponding experimental bench was set up to test the performance of the constant temperature drying mode. The air supply temperature of the heat pump drying device and the bypass rate of the drying medium were adjusted by the control system, and the drying experiment was carried out under different operating conditions to test the effects on the wet cotton cloth. The results showed that the specific moisture extraction rate (SMER) of the heat pump drying system decreased with the increase of the drying temperature, and increased with the increase of the bypass rate. The maximum value was 2.47 kg/(kW·h). The coefficient of performance (COP) exhibited a rule opposite to that of SMER, with the maximum value of 4.24, and the different drying media had different optimal bypass rates.