Unless you're really slow, you should have no problem. Cold (depending on your definition of "cold") probably cannot be avoided, but you want to try to avoid snow if you can. You'll avoid most chances of trouble if you're through Colorado by the end of August. But, depending on your (unspecified) route (you didn't even say if this is coast-to-coast or not), your cold-weather challenges aren't done there. If you're on the TransAm, Yellowstone NP will be your next biggest chance of problems, and you're still not done with possible cold. Most cross-country cyclists can complete the trip in three months or less, so you'll probably finish the first week of September or earlier, and most likely (but not certainly), you'll be fine.