A 2 degree Celsius sudden swing should be tolerable for fish, I wouldn't go much more than that. A gradual change over time will be preferable.
I now live in Panama, only a few degrees of the equator, and have found temps are much lower than I thought they'd be.
I have a 10,000 gal pool, and at night thru morning it can drop into the low 70s, but by late afternoon the surface temp can hit almost 90'F, but still cool 3-4ft down.
And during the rainy season remain low weeks at a time.
I also found it interesting, that in the forest, streams and small pools under the canopy can also be quite cool, and especially if influenced by mountain runoff.
Slow moving water without cover, and sun soaked pools are more likely to have major temp swings day to night. Although this lake in Panama that contains Peacock Bass and other cichlids, was quite cool, and snorkeling for me, ended up being quite short, without a wet suit.
Ocean currents also seem to have a strong effect, the Humboldt current that runs north from Chile to the Galapagos seems to hold temps down in countries the hug it, and it sometimes influences temps all the way here in Panama.
So my point is, I believe we fish keepers sometime tend to keep our tanks much higher than needed with a few exceptions. (especially when you consider many of the fish pathogenic bacteria thrive at temps above 82'F (columnaris for one)).
Water in Lake Natron in Africa, because it is so shallow, and lacks cover has normal temps in the 90sF. And waters inhabited by Nandopsis haitiensus in Hispaniola, often average in the high 80s.