Do fish go into shock if they are moved to warmer water?

Yes and no. It's really more about how quickly the changes come about. A very quick change of as little as 5 degrees can kill a particularly sensitive fish but if the change were to happen a couple if degrees every 15 minutes or so the fish would survive a wide range of temperatures. Some Bettas are able to live well in 50 F water and also in 90+F water. In the wild some of the small ditches these fish live in can get to over 110 F and the fish live through it. It's all about the speed of the change.