Thermostat reading higher than actual temp

[Rwunder]

One of my Nest thermostats consistently reads 5-6 degrees warmer than the room.   For example the thermostat reads 77 degrees when the room is actually 72 degrees. This only started this Summer and we have had the thermostat for years. Any ideas would be appreciated. 

[Frustratedddd]

Does the display feel warm when touched?

Sounds like the battery has had it's day if yes.