Thanks for the reply!!!
I am sharing what happened today.
I came to office and pressed the power button on Mini. The light took time to show up. Now this is first indication that fan will go loud. And yes, after 5-8 seconds, when white light came on CPU, the fan become aloud. I restarted from the login screen and that didn't help. So, again from login screen I shut down the Mac.
Every time, the below process has helped me, including today.
When my Mac shut down completely, I switch off the power button & take out all connections & then reapply all connections and switch on the power source. Then I press the power button of Mini and it boot normally.
So it might be the power source itself coming from the switch board?? Can't be sure though.