Soil temperature is most important in my (untrained) opinion.
If you have a lot of rain at this time, my principal concern would be the potential for other grasses to be strong and outcompete a still-dormant Bermuda/couch. Poa and rye would love the spring rains, as would broad-leaf weeds. Your superintendent's turf programs will be tested in such circumstances.
If you get a warm rain, it might help soil temperatures. If you are getting cold showers, then it won't.
James B