Remote thermometer in wrong place?

I recently had a new heat pump installed. The installer did a good job but one thing is concerning me. I had them install a VisionPro thermostat and an external thermometer to control the crossover from heat pump to oil/fossil.
The problem is, they installed the thermometer inside the service cover of the outdoor compressor unit. When it is cold out, and the compressor has been running, the temperature reads about 10 degrees too cold. I assume this is because of where it is mounted. However, this is one of the installation options listed in the outdoor air temperature sensor manual.
Am I being too picky? Or should I ask them to mount it on the side of the house? Technically they did mount it in one of the recommended locations, but I think it would be more accurate on the side of the house.
Opinions?
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We install them inside the unit also. Seems to last longer and "act" better that way.
If you mount it on the side of the house, you could have a real cold afternoon and if the sun is beating down on the bulb/sensor, you aren't going to get a true reading there either.
If you think it's kicking in/out at an undesirable temp, change the setting.....
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