My back fan has been coming on in my 2012 Prius. I just bought it, have had it one week. In my Gen 2 Prius, the fan in the back was a good indication that my hybrid battery was about to die (and it did). Are the fans in the back of the newer generations louder? Or should I be concerned ???
The fan does come on to cool the battery. I find the fan in my 2015 car to be louder than my gen2 cars.
I have a Gen 3, but I don't hear my fan very much at all. I would check to see if it needs cleaning. Since you did by it used, it may just need cleaning.
Strange as it may sound, I really notice the gen3 car's fan a lot more than gen2. I rarely notice the gen2 fan on, but lately my gen3 fan comes on quite a bit a low speeds. But of course my gen3 is black and it's 100 degrees outside.
I've started hearing it in the summer.... last year or year before. Prior to that, it only came on once when I went through valley and it was 36°C outside and I just came down a hill and topped up the battery. So yeah I've been hearing the fan too, definitely moreso than in the Gen 2 (which was only once... when it was 35°C and it was parked in the sun for 2 hours or so) but I've been hearing it for at least 2 summers, possibly 3.