A/C blower taking its sweet time...

2003 T&C, A/C blows really cold air...when it feels like it. No problems until we had a major heat wave and very high humidity not too long ago. More often than not, when it's more than warm, or humidity levels are above average, the blower wants to take its time to kick in. It generally will after I drive it for several minutes and will work fine after it gets going. I'm wondering if the heat wave/humidity may have done some kind of damage that would be easy to fix. Any ideas? You guys have been lifesavers more than once, so thank you in advance. Thanks!