The thing about rain in tropical areas is that it's falling through tropical air. Air which is going to be warmer than the water in which the rain is falling.
So, there's little reason to think that rain is going to chill the water significantly particularly when you consider the tiny proportion of water contributed by falling rain in a tropical lake.
Rain is a poor example, but floodwaters might well be considered a valid factor. Indeed there are a number of species which spawn during flood conditions.
Though of course there is no reason to believe that condtions which might initiate spawning are conditions which are pleasant for your fish.
Fish aren't like people, they don't like romantic settings and mood music before breeding. In many instances fish spawn in adverse conditions to ensure their species survive.
There's no reason to consider the practices of pet stores in any way ideal; quite the opposite in many cases.
An ideal temperature for your fish is a steady one. So, try to match water change temperature to that the fish are currently in.