Hi,
This could be a number of things. First off the light means that the differential is too hot in the rear. This is either caused by a faulty sensor and it is not actually too hot or it is too hot and it is disabling the system.
Due to this happening after you drive for a bit, I suspect it is getting hot. There is a clutch inside the rear end that gets applied and released depending on driving conditions. If this clutch is applied when it shouldn't because it is sticking or some other issue then the heat will build in the rear end causing this issue. Also, if the clutch is just slipping and not fully engaging when it should, it could cause this same issue.
I attached a lot of information to explain this system in more detail. However, I think the next step is to drive the vehicle with a scan tool hooked up and see what the temperature sensor is actually saying and see if there are any codes in the system. If there are that will give us more to go on.
Please let me know if you have questions or what you find with the codes. This could be as simple as needing to have the fluid changed or it could be more serious.
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Thursday, October 24th, 2019 AT 2:18 PM