The primary cause of failure to germinate seedless watermelons is rewetting the seeds before emergence. They need evenly moist not wet soil. I doubt your soil was all that cold in May but it sounds like it was wet. Did you get rain soon after planting?
I’ve seldom had any issues getting melons up since adapting the methods outlined here Seedless watermelon emergence 6 days outdoors mid March
That includes many yrs of planting seedless watermelons outdoors in March when our average air temperature is 54F. Warm and evenly moist soil is the key. I never water after the initial watering at planting until after the plants have emerged. If it works for seedless, normal melons are a breeze.