Prokaryotic organisms are able to grow at far higher temperatures than are eukaryotes.
Archaea are known to group, among some mesophiles, the most extremophiles organisms (es. Pyrococcus furiosus), but also some bacteria can reach quite high-temperature habitats, such as Thermus aquaticus.
Eukaryotes instead are far less tolerant in terms of maximum growth temperature.
Also most of the hyperthermophiles are chemoorganotrophs or chemolithotrophs, being autotrophs (Cyanobacteria) far less heat tolerant.
My question is about the physical or chemical limitations that block eukaryotes from adapt at extreme habitats like prokaryotes do.