At least this year, in Illinois, where the average temperature is actually below March's—and it's still above normal:
The statewide average temperature for April 1-22 is 12.3°C. The statewide average temperature for March was 12.8°C, based on the latest numbers from NOAA. That means that April was almost a degree [Fahrenheit] cooler than March. What makes this even more freaky is that the April temperatures are still 1.9°C above normal!
BTW, the statewide normal monthly temperature is 4.8°C for March and 10.9°C for April, a ten degree [Fahrenheit] rise.
State Climatologist Jim Angel concludes by pointing out that we've only had one April in recorded history that was cooler than March, back in 1907. (Recorded history goes back to 1895.)