Generally we are warming up by April and May can have some toasty days - hit the 90s. Since you're a thru-hiker and desert dweller, I'm guessing you'd be OK - with certain precautions. Of course, the more miles you can do in a day, the sooner you'll be past the desert and into the high country. But, if you are in the desert during the higher temps - more water, SALT, and hike early / late, taking the warmest parts of the day to hang out. Use an umbrella. But overall, hitting the trail in early April should be fine.