Can I use polyurethane to coat a painted wall tile and safely use as a trivet?
The clearcoat won't buy you anything for temperature resistance. It's not like you can put a high-temp clearcoat over a low-temp-vulnerable paint and have that work out.  Both the paint and the clearcoat will need to be high-temperature rated, since it'll be encountering worst-case 400F/200C or so from the bottom of a fry pan.  

By the way, you need more words.  You're cutting off the noun, like using the word "cell" to mean "cell phone" or "built-in" to mean "built-in cabinets".  This doen't work with polyurethane because it is ambiguous - you have polyurethane paint, polyurethane stain, polyurethane sheeting, polyurethane panels (glass) etc.