It's generally accepted that it's good to get the temperature of your new water to match the temperature of the tank water before introducing it. You don't want to change the temperature of the aquarium too much when you add the new water, or you risk a temperature shock that can kill fish.
Are there quantitative recommendations as to how much the temperature of the water can vary before and after the water change?
My own research shows plenty of individuals declaring "0 temperature change is the only acceptable answer." Others argue that a sudden rainstorm drops the local temperature of water, so fish are used to some change. The aquarium wiki has an uncited claim that you want to avoid instantaneous changes greater than 5 °C (8 °F)
Are there any studies which have shown quantitatively what the effects of instantaneous thermal changes on a reasonable order of magnitude have (I'm thinking like 0 °C to 8 °C changes). I've seen studies which covered the effect of 20 °C changes, which are obviously dramatic, but nothing on the smaller changes.
I'm particularly looking at freshwater tanks, but saltwater numbers may be useful for others.