"Auto" setting on climate control not working properly

I just bought a used 2003 Prius, after my beloved 2001 Prius met an untimely demise. I loved to use the "Auto" setting on the climate control in the older car. Unfortunately, it isn't working properly in the 2003.

What I'm experiencing is that on the Auto setting, the car just blows maximum hot on the high fan setting, which become unbearable after about 60 seconds. This behavior is unchanged, unless I turn the temperature dial all the way down to a few small clicks above the minimum temperature. Then the air suddenly changes to cool, on a medium fan setting. Meanwhile, I can manually adjust the fan settings, but I would like it to work the way it did in my 2001.

Does anyone have any ideas why the "Auto" setting isn't working, and what it will take to fix it?