The phrase "set one's heart on something" is correct and usable in written English. The phrase means to have a strong desire to have or do something. For example: She had set her heart on going to college and nothing would stop her.
For Christmas, Colin Stovel, 11, had his heart set on one of Lego's new electronic or science fiction sets, like Star Wars or Mindstorms.
Why set one up then?
Don't ignore the idea of working for them even if you have your heart set on one day working for a global, blue chip employer.
If your heart is set on wearing one, you can pick up a Maratac watch band for about $17, and stick it behind the clip on the Nano.
There is more to overtness than wearing one's heart (or mind) on one's sleeve.
When the word "love" comes round in sets of three, Mr. Morris sets one set with three deliveries of the conventional love gesture (hands on heart), another set with three jumps (i.e., for joy), and yet another one with three lifts (i.e., it's you I love).
You hop on the Googlenets with your heart set on snapping up one of these 32GB cards to call your own.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.