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I think it may depend on the species and other health related factors. Truth be told, tropical fish can probably tolerate a fair range in temperatures especially if the change is gradual. Of course I have no idea how much of a change can be tolerated but I can say that my swordtails seem very resilient. As an example, I have a little 5 foot kiddie pool turtle 'pond' in my unheated basement (55°F in winter). I have had swordtails survive in there even when I have done water changes with cold well water. Now I surely wouldn't recommend temperature shocking fish, but I wouldn't panic if/when the power goes out... I think a bigger issue than temperature just might be oxygen depletion for both fish and beneficial bacteria (but this is just my impression). ;-)I only have temperate fish but I know even a degree change can cause shock