You should be able to put the instrument in the sunshine and have accurate data. Under a tree is not where you want to take a temperature and humidity reading. You want an open area with full sunshine and an open sky for true temperatures at night as well. If the fan is not running, your temperature will be 5-10 degrees over. If it is not running optimally it can be 3-5 over. If your unit is beyond warranty, I would paint the bottom. It makes a great difference and allows for sunshine to hit the housing without tainting the sensor with heat. If you are still in warranty and are having temperatures taht are too high, contact the company. There have been many with motors freezing up.
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