Whenever you're driving at least 20 mph, you don't need fans at all. So if your engine temperature is OK while you're driving around (especially climbing big hills), then your thermostat is OK. If your thermostat sticks open, then your engine will take forever to warm up.
The only time you need the fans is when you're going real slow (or stopped) so there's no air going naturally thru the radiator.
So now, with the switch A shorted, is your engine temperature gauge behaving normal? If so, your thermostat is OK. The only downside to shorting this, is how quickly you'll wear out the fan motor. (You could use a toggle switch.)
Finally, remember that the fan switch isn't supposed to come on at the same temperature as the thermostat. Your gauge will have to move up (above 1/2 scale) before the fan switches on. As long as it doesn't go very close to the top (red) part of the gauge.