The IntelliFlo does have a temperature sensor, but it doesn't report that temperature to your EasyTouch (ET) or ScreenLogic (SL). The pump uses that sensor for it's own freeze protection (which is different from the freeze protection you might have setup in your EasyTouch).
The IntelliChlor (IC) also has a temperature sensor, but it doesn't report a number to ET or SL either. It uses it internally to determine if it should produce chlorine or not, and if it thinks the water is less than 52°, then it won't. And the IC's cold water LED will be red. The IC doesn't know, or care, what temperature the ET or SL thinks it is, it'll shut itself down all on its own (it doesn't even need an ET installed to do that). It will, however, report a cold water shutoff back to the ET, in the form of an alert you should be able to see in SL (but not the actual temp reading).
There are ways to measure what the IC's temp sensor is doing, with an ohm meter. I think Jim knows how to do that. But an alternate method is to measure the pool's temperature with an accurate thermometer and observe what the IC is doing. If the IC has power, and your pool is at or above ±52° and the IC's cold water light is off, then that's good. If the pool water is below ±52° and the SWG's cold water light is red, then that, too, is expected. And I wouldn't worry too much if the threshold is a bit higher or lower than 52°, even up to 5° off (just my gut on that). Now it if was off much more than that, then that's something to look into. The IC's temp sensor can be tested and/or replaced without too much trouble.
The trick to that troubleshooting is to make sure your thermometer is accurate. A typical floating pool thermometer can be off by 5° easy, so that would skew your test.
When you say the temperature is off "3-10 deg," are you referring to the air temperature or the water temperature? Either might be mis-adjusted from the actual temperature.
Either can be adjusted, using the ET's settings. Again, you would want to compare the air temp reading or water temp reading to a known accurate thermometer and adjust accordingly. You can't assume either ET reading is accurate from the factory.
And possibly making matters worse, the accuracy is location dependent. Jim mentioned a typical location for the ET's air temp sensor is close to the ET. That's where my installer put mine, but my air temp reading was really far off, and erratic. So I added a length of wire to the sensor and relocated it in the shade, just under my roof eve, so that the sun couldn't get at it.
Air temp sensors need to be in the shade, with good air circulation, to produce a reliable ambient air temp. You won't get good air temp if the sensor is in the sun. Mine was in the shade under the ET, but my ET is mounted on the west side of my house, so I think the sun hitting the ET and the surrounding stucco was affecting the air temp sensor. And I think that's why it was off, and erratic. The reading was OK in the morning, when everything was cool, but got wonky when the sun hit that wall. Now, under the eve, it's very stable. I adjusted my air temp offset (in the ET settings) to match the local weather report temp, and confirmed that with another air temp sensor I have elsewhere in my yard. All three temps match, so I'm pretty confident my air temp is accurate (or at least close enough).
I did the same with my pool temp sensor, matching that to my pool thermometer. It doesn't really matter to me that the two might be off a degree or two from actual temp, as long as they are the same. When either says 80°, my body knows what to expect. If it's actually 82°, or 78°, so be it.
And finally (finally!), if your SWG is producing chlorine (which you can double-check with an FC test or two), then it's fine. FC production drops the colder the water gets, so if your SWG was trying to produce in water too cold, you'd see a decrease in chlorine production. So: no cold water light + measurable chlorine production = your SWG is just fine.