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Joyce - I specialize in out of production Duo Therm parts. I do not have that number but I do have a 310 5604.023. It has a flat 10 pin connector plus 3 wires - Green, brown & purple on the back. The front upper half has three buttons - Mode -Up -Down with a small digital screen above. To the left of the screen graphics "Acturl-Cool-Heat".
The lower half has two slide switches. The left one is marked Cool-Off-HeatPump-Aux Heat.
The right one is marked "High-Low-Low-High" opposite of Auto and On.
Sometimes part numbers will change because of color or trim. Is your thermostat the same as this?
contact me at whendrix@aol.com
Is yours the same