On the top of the AC compressor is a two wire connector, it activates the Electric Clutch to engage the compressor with fan belt
Unplug connector and then start the engine
If compressor is still "on" then the clutch is bad, always engaged, mechanical issue
If its off now then you have an electrical issue
The AC compressor should be on if AC(or AC Max) is selected on the dash switch but ALSO if Defrost or Floor/Defrost or Panel/Floor is selected, it helps dry the air in the cab, so there are 5 positions with AC on
There are only 3 positions when AC compressor is off, Panel only, OFF and Floor only
In 1997 AC systems the dash switch sends 12volt out(with AC on) to the pressure switches, if a pressure switch is "open" then AC compressor won't come on
After going thru the pressure switches the 12volts splits and goes to the Computer AND to the AC relay which passes the 12volts to the Clutch on the AC Compressor engaging it.
The AC Relay is a default relay, it always passes the 12volts to the compressor UNLESS its activated by the Computer to Cut Power to the compressor
Its called the AC WOT(wide open throttle) relay, computer activates this relay to cut power to compressor when you "floor" the gas pedal, this gives best engine power for passing or...??, for whatever reason the driver needed to floor it for, lol.
AC WOT relay is in the engine bay Fuse box
Temperature control in the cab is not related to AC on or off for the most part
Temp control is done by the Blend Door, in 1997 this uses an electric motor on a "door" inside the dash to direct air from the fan thru the heater core(HOT) or away from the heater core(COLD)
The Blend Door Actuator(motor) was a common failing in Fords, Rangers are no exceptions
So if you are blowing cold air with temp knob turned to HOT then its a Blend door issue, even if AC is on, which might be unrelated issue