"heavy thinking" is correct and usable in written English.
You can use it to describe deep or intense thought. For example: "I spent the evening in heavy thinking, trying to solve the puzzle."
But hey, too much heavy thinking going on here and not enough drinking.
A person can't discover the theory of general relativity in a dream if he isn't a physicist who's done some heavy thinking about the subject beforehand.
The cafe, a cheery-looking, brightly decorated counterpart to Mr. Forgione's other restaurant in the store, emphasizes salads, big-bowl soups, little pizzas and the aforementioned panini, but the heavy thinking has gone into the desserts.
She has a bus and I don't, so it's been all I can do to keep up with her for the last couple of weeks, on top of doing some heavy thinking about Afghanistan.
Early, early mornings are when Barch carves out protected time for heavy thinking and data analysis, she says.
Let others provide the public face of Web searching and the "portal" that draws people into the Web; Inktomi will do the heavy thinking in return for a percentage of the advertising revenues or a flat fee of a fraction of a cent per search.
"He told me he had used a product because he had heavy legs, thinking it was harmless," Lavenu said.
Don't, a colleague advises ahead of me meeting Joan Bakewell, go heavy on "thinking man's crumpet" or Harold Pinter.
I was on recently about having had a heavy day, thinking about losing the kids to get myself upset for a scene.
Our palms are sweaty, knees are weak and arms are heavy just thinking about it. .
