"burning curiosity" is correct and usable in written English.
You can use it to refer to a feeling of strong, intense curiosity about a certain topic. For example, "His burning curiosity led him to research the topic in greater depth."
He wished he could feel something solid and real about Dylan Riley's murder — anger, indignation, a burning curiosity, even.
I tell people they're the Pablo Picassos and Zelda Fitzgeralds of the cat kingdom; big personalities, burning curiosity.
If you want to be an astronomer "you need to be someone with burning curiosity about the world," he says.
Avoiding easy propaganda, the production worked because it was rivetingly specific about Rachel's burning curiosity and the practical details of Palestinian life.
He emphasised the burning curiosity of scientists and the wonder of the science they do – how Newton could link the fall of an apple with the movement of the planets, uniting the local with the universal.
Residents, many of whom express a burning curiosity to know the satirist's identity, may be surprised to know he does not live in the neighborhood.
Templeton had a burning intellectual curiosity, which played at Graham's one insecurity, his middling intellectual firepower.
So, burning with curiosity, you engage in the investigation whether P, expecting to find tranquillity when you discover whether P; you end up not discovering whether P but rather suspending judgment whether P, and much to your surprise, tranquillity still follows.
7) Stop yourself from flipping through your kid's inbox if they make the mistake of leaving their Facebook page open Just because you are burning with curiosity to read all of your kid's personal messages does not mean you should open up your daughter's inbox and read every single message ever sent from her inbox.
You need to have that burning desire or curiosity.
