MacBook Air fan noise and sudden shutdown

I use my MacBook air only occasionally, so it is not heavily used. I just recharged it for getting ready to use. After a while I found it making noise like a fan, never done that before. I unplugged it, then proceeded to open and log in, successfully. As I was not ready to use it, I placed it in another location and went out for a while. When I came back, it was still warm and fan noise. I opened it, closed it, set it down, and fan stopped. About an hour later I was ready to use it, opened it, got a flash of opening scene, then it blanked out. Now it will not respond to start up. Is it dead?

[Re-Titled by Moderator]