Your experiences make absolutely sense and are what I would expect. Slower response is expected, how much depending upon the insulation effect of the bag. But eventually it will be correct. If sunlight hits the bag, you will for sure get a significantly higher temperature obviously. A plastic bag in sunlight is identical to a greenhouse. Correct reading in sunlight is a challenge no matter how the sensor is encapsulated. Have you seen professional temperature sensor stations? They are big with several large white discs in a stack to create a proper shielding to sunshine. When I suggested a plastic bag, that was for rainy conditions with no sunshine. I agree that a waterproof unit is absolutely to prefer, but as long as LM4 does not support any such devices, WS07/WS08 is what we have for LM4, and using a plastic bag when rain is a workaround that I can live with.
I also have the Garmin Tempe sensor connected to my Fenix 3 watch. It is strange that the Tempe case is black, since black absorbes sunlight while white reflects sunlight. That is why professional temperature sensor stations are white. The Tempe sensor is one example of a completely sealed case with no direct contact between the sensor and ambient air. That is why it is waterproof. So Tempe, just like WS07 in a plastic bag, depends upon the whole unit to cool down/heat up to reach ambient temperature before you get correct reading.
I also have the Garmin Tempe sensor connected to my Fenix 3 watch. It is strange that the Tempe case is black, since black absorbes sunlight while white reflects sunlight. That is why professional temperature sensor stations are white. The Tempe sensor is one example of a completely sealed case with no direct contact between the sensor and ambient air. That is why it is waterproof. So Tempe, just like WS07 in a plastic bag, depends upon the whole unit to cool down/heat up to reach ambient temperature before you get correct reading.