The clue is in your description!!
The fans "constantly cutting in", this shows they are doing what they should, trouble is they are drawing warmer ambient air through the rad when on so there is not so much cooling effect as with colder air, the fact that they go off shows they are able to do the job effectively, so long as they are cycling on and off that is fine.
The span or heat range of the std fan switch is terrible, measuring some 11C - 13C, on mine when I used one.
Don't worry about hot, my fan comes on at 95C and goes off at 92C, that is what I set it to(aftermarket ecu), it just sits there cycling on and off all day.
I came across a car accident two days ago, 31C outside left my car running,(with hazzards on and lights on as was on a bad bend to warn others) for 1 1/2 hours, didn't miss a beat.
Temps around this are NOTHING to worry about, and will NOT kill headgaskets, don't relay on the temp gauge, these are chronically innaccurate, my fans always come on at correct temp and this can be anywhere on the gauge from middle of the M to just above the N !!
So long as the fans are rewired and everything is as it should be don't worry, it's normal, if they haven't been rewired order a head gasket and bolts etc now, as you're going to need it!!
tabetha