Warmth sticking around through the end of September?

It's very well possible.  The outlook from the Climate Prediction Center highlights most of the United States with the possibility of temperatures remaining above average through the end of the month.  Keep in mind that this doesn't necessarily mean that every single day will significantly be above average, because by the end of September the average high does drop to 70 degrees.  However, the prospects of a big drop in temperatures in the near future doesn't look too promising.

Temperatures will drop for the start of the weekend following a strong cold front Friday afternoon.  After that, highs look to even out right around average - in the middle 70's for next week.