The optimum growth temperature for extreme thermophiles is:
Thermophily classification uses cardinal temperatures minimum, optimum and maximum for growth. Mesophiles optimum 20 to 45 degrees encompassing most pathogens, thermophiles 50 to 70 degrees like Bacillus stearothermophilus, extreme thermophiles also called hyperthermophiles optimum above 75 to 80 degrees growing up to 113 degrees in Pyrolobus fumarii near deep-sea hydrothermal vents where pressure keeps water liquid. Adaptations include proteins stabilized by increased ionic networks and tightly packed hydrophobic cores, chaperonins like thermosome retaining activity at high temperature, membrane lipids composed of ether linkages and tetraether monolayers spanning membrane preventing melting and proton leakage, reverse gyrase introducing positive supercoils stabilizing DNA against melting, increased GC and 2 prime-O-methylation in ribosomal RNAs conferring rigidity. They thrive in Yellowstone geothermal springs, deep sea vents, compost and volcanic soils where lower temperatures are suboptimal. Specialized anaerobic high-temperature cultivation is required. Their thermostable enzymes especially Taq polymerase from Thermus aquaticus revolutionized molecular biology by enabling polymerase chain reaction, illustrating profound biotechnological significance of thermophiles in research and industry.
Ref: Prescott's Microbiology, 11th ed., Chapter 7: Extreme Thermophiles and High Temperature Growth Optima.