I think you're on the right track with the moisture sensor. The PartSelect website has the part, and they offer Q&A for their customers. Here's a customer question that applies to your situation.
Unit works on timed dry. Does not heat on sensor dry. Do i need a moisture sensor.
For model number 110.86582110
Hello Art, thank you for your question. The moisture sensor would be the first part I would suggest replacing. A functioning moisture sensor is imperative for the sensor dry setting to work properly. I hope this helps!
Here's a link to the part and page in question.
Personally, I would shop around, as it's quite likely you can find that same part cheaper on other sites such as eBay or Amazon, but this is definitely the right one for your dryer.
Obviously you'll want to make sure it doesn't just have a wire that fell off or something, so if nothing obvious can be found, replacing the sensor is your best bet here.