It certainly doesn’t have a temperature sensor built-in. I don’t have a tempe to test but I did check and it’s not selectable as a type on the sensor search menu - however, there is a ‘search all’ that may find it.
It's true that edge explore doesn't have a built in Tempe for Garmin Tempe sensors. Instead you have to download a third party Tempe app from Garmin connect store. There are up to 3 different Tempe apps in connect store. And they work perfectly when paired with the Tempe sensor.