Many therapeutic hypothermia recommendations have been reported, but the information supporting them is sparse, and reveals a need for the data of target therapeutic hypothermia (TTH) from well-controlled experiments. The core temperature ≤35°C is considered as hypothermia, and 29°C is a cooling injury threshold in pig heart in vivo. Thus, an optimal protective hypothermia (OPH) should be in the range 29-35°C. This study was conducted with a pig cardiopulmonary bypass preparation to decrease the core temperature to 29-35°C range at 20 minutes before and 60 minutes during heart arrest. The left ventricular (LV) developed pressure, maximum of the first derivative of LV (dP/dtmax), cardiac power, heart rate, cardiac output, and myocardial velocity (Vmax) were recorded continuously via an LV pressure catheter and an aortic flow probe. At 20 minutes of off-pump during reperfusion after 60 minutes arrest, 17 hypothermic hearts showed that the recovery of Vmax and dP/dtmax established sigmoid curves that consisted of two plateaus: a good recovery plateau at 29-30.5°C, the function recovered to baseline level (BL) (Vmax=118.4%±3.9% of BL, LV dP/dtmax=120.7%±3.1% of BL, n=6); another poor recovery plateau at 34-35°C (Vmax=60.2%±2.8% of BL, LV dP/dtmax=28.0%±5.9% of BL, p<0.05, n=6; ), which are similar to the four normothermia arrest (37°C) hearts (Vmax=55.9%±4.8% of BL, LV dP/dtmax=24.5%±2.1% of BL, n=4). The 32-32.5°C arrest hearts showed moderate recovery (n=5). A point of inflection (around 30.5-31°C) existed at the edge of a good recovery plateau followed by a steep slope. The point presented an OPH that should be the TTH. The results are concordant with data in the mammalian hearts, suggesting that the TTH should be initiated to cool core temperature at 31°C.