What are the benefits of thermal imaging,say on elec.machinery?

Answer 1

In any moving machine heat is a sign of inefficiency, so if you have a thermal image, you have an immediate picture of where energy is being wasted.
In extreme cases these images help identify where bearings are wearing out (and have slack generating movement and heat), where lubrication needs applying (to stop wear) or even help understand what is making a component fail (if heat from pumping a hot liquid is being conducted from the pump to the motor, thinning and removing lubricants etc)

Answer 2

You can see where the hot spots are and prevent burning out motors or gearing