So I've spent most of today looking for the cheapest flights for our upcoming trip to the US: four weeks of unadulterated nature and wildlife road-tripping

But flexible dates and flexible destinations are a bitch.
We want to do the western part of the south west US, from Denver down south and then up to Salt Lake City or a trip from Denver down south and then back to Denver again. It'll be the end of September, so we want to do the mountainous regions first and the hottest/more desert like regions in October (I cannot tolerate heat).
But I'm worried: I know nothing about those regions and so I don't know if the 22nd of September to the 19th of October could give us weather problems. Any experts out there?