DualImage.php uses the GD library to construct a combination of two PNG images into one image for the 6hr primary forecasts for the 12hr period. It usually completes in <100ms as the GD routines are quite fast for doing image merging. Similar GD routines are used in the thermometer.php to construct the thermometer image with current/max/min displayed.
Since you're not running a Saratoga template, my usual diagnostics aren't available.
What is the server's operating system? PHP version? GD library version?
Lastly, how did you ascertain that DualImage.php was consuming the CPU time?