According to the 2011 core rule book: "A force cannot be assembled with two unique characters with the same name, the same set symbol, and the same collector's number."

Does this mean I can have one of each of the HoT Warriors Three figures and one of each of the Fast Forces Warriors Three figures on a single force?

In this case unique refers to a silver ring around the dial.
No more than one figure of the same name and set number with a silver ring can be on the same team.

Yes you can.
The 3 from the fast forces set have a different set symbol.

That's exactly what it means.

Stranger examples are the Classics ultimate Nick Fury and the Sinister Unique Nick Fury. Same name/dial/sculpt, but different set/collector number. The same goes for the Infinity Challenge Uniques that were reprinted in Universe; you can run 1 of each.

But yes, both sets of the warriers 3 may be on the same team.