Hi ThomasMD.
Yes, in a dry climate 20F is about the limit for evaporative cooling. So you are getting about as good cooling as can be had with your sprinklers... a well designed setup.
Note that if humidity rises outdoors, you won't get that 20 degrees. So temperature only control is perilous. You'd be better with both temp and time, better yet check outdoor humidity and temp also. This brings to mind the use of an Arduino with the appropriate sensors and a solid state relay to turn on the valve and when to turn on the fan based on inside and outside temperatures, humidity, time. It gives you total control and additional greenhouse automation could be added as it suits you. It's interesting and fun for those with some technical interest.
The online support is quite good, the hardware is dirt cheap. Let me know if you are ambitious enough to try and get stuck. I'm a retired, disabled EE.
Best Wishes,
Bruce M
Concho AZ