Between 5 and 63 Celsius. That's why we keep food in a fridge below 5 Celsius and cook at over 63 Celsius. The temperature bacteria grow fastest at is 37 Celsius which is also human body temperature.

Thermophile bacteria thrive at higher temperatures, between 45 and 80 °C and some even higher than that (hyperthermophile). The bacterialike Pyrolobus fumarii likes heat above 110°C and Strain 121 is found to reproduce at 121 °C and survive until 130 °C. Some genuine bacteria resist temperature above 100°C, and 121°C is needed to kill Clostridium botulinum. At 150°C the DNA is destroyed, so any imaginary bacteria that could resisting such temperature must have an unknown constitution.

So, 45 to 100°C is the temperature that the thermophile bacteria like.

Thermophile bacteria thrive at higher temperatures, between 45 and 80 °C and some even higher than that (hyperthermophile). No limit is known, and new species are discovered, but at 150°C the DNA is destroyed, so any imaginary bacteria that could resisting such temperature must have an unknown constitution. A variety of bacterialike Pyrolobus fumarii is found to reproduce at 121 °C and survive until 130 °C. Some genuine bacteria resist temperature above 100°C, and 121°C is needed to kill Clostridium botulinum.