Just to point it out, what bitmask already mentioned.
Danke schön sounds awkward in any sentences. I will copy his example:
Danke schön für das Eis!
It's not completely wrong, at least in colloquial use, but I think, if you want to phrase it like this (in written text), I would place a comma:
Danke schön, für das Eis!
Now you have an interjection Danke schön and in addition an separate phrase explaining what for you said thanks.
So, Danke schön is more just an interjection and stands alone. Example: You get an gift and you hug the person while saying:
Danke schööööön!
(Most people stresses the ö extremely ;p)
In written context, imho, you use Danke schön only for direct speech.
Als ich Max das Geschenk überreichte, sagte er "Danke schön".
but better would be
Als ich Max das Geschenke überreichte, bedankte er sich bei mir.
In formal context or whenever you want to phrase a full sentence, you take Vielen Dank. That sounds much better:
Für die Aufmerksamkeit noch vielen Dank, aber das wäre nicht nötig gewesen.
Although this isn't any good example, because most (or every) native speaker wouldn't phrase it like this. I just did it this way to show that is is theoretically possible.