Featured Dome light fuse / J6 Connector / slow battery drain

That amount of power is similar to that of one of the old incandescent bulb nightlights. How hot it will be in a circuit depends on the area that is radiating that power. If it is all dissipating in an isolated electronic component one quarter of the size of a grain of rice it may become so hot that it will burn out. If the electronic component is about 1 cm square and is thermally bonded to a 1" square finned heat sink that whole assembly would only be slightly warm.

 

Maybe—if you're very sensitive to warmth and there's no draft to distract you, and so on. Or if you know somebody with a thermal imager.

Keep in mind that because of the way the instruments are a projection, the actual place you'd be expecting warmth won't be where the digits are displayed: it'll be nearer to you, under the dash top.