I would shut off both filter and heater during a water change. If the heater is not fully submerged, but some of it is exposed to air, it may very well crack. I leave the light on, this is better for you and the fish. Sudden changes in brightness affect fish a lot, and they require about 30 minutes to adjust. So by turning off the light, and then crashing around in their tank, you are actually shocking them a fair bit. I wait an hour after the tank light comes on before I will start a water change, or any work in or even around the tank. One way to easily deal with this is to have a small power bar that has a switch [you can get these for a couple dollars at Home Depot] with just the filter and heater(s) plugged in it; this bar is then plugged into the main outlet, where the light is also plugged. Turning off the small power bar shuts off the filter and heaters but not the light.
Some people use cold water for water changes, with no hot/warm at all. I would find this terribly cold, given my very cold tap water [just did a test now as I was curious, and it is running at 50F or 10c], and while they say their fish have no issues, I prefer to use a mix of cold/hot and have the temp a bit cooler than the tank; I use my hand to adjust the tap temp for this, with a small container of tank water with me so I can check back and forth.
If I used just cold, with 50% changes, the temp in my tanks would easily lower by close to 15 degrees (applying TTA's math). That means that my 78F tank would lower to 63F, and within the space of a few minutes. Also, the heater has to work very hard to bring this back to 78F and it would take hours. Sounds too risky to be advisable.
Temperature changes in the Amazon rainforest are not sudden, but gradual. There is the diurnal change, over a 24 hour period, and fish seem OK with that. But remember also that in most watercourses, the water is not uniform temperature, but cooler in the middle and lower down, and warmer at the surface and near the banks, and fish are able to move around to suit their whims. Also water heats and cools much more slowly than the air. The seasonal fluctuations are significant, but this too is gradual and once a year, not every week. And I would suggest that the difference is probably minimal compared to what we have been discussing here. Goulding et al (1988) gave the annual temperature range for the Rio Negro to be from 28 to 31c (82-87F) which is not much, and this river floods into the forest for hundreds of square miles during the wet season. The ground is warm, also affecting the water temperature.
I have a 2-3 degree F drop using my method. I almost always see spawning from more than one species next morning.