Left second week of April twice. Snow at the top of the Pyrenees. The first year, it rained on and off for three weeks, all the way to Leon. Mornings were mostly +5C and gray, afternoons +14 ~ +18. We had frost one morning, and it was +2 with a strong wind the morning we left Burgos. The second camino was another story altogether. Rain and +10C the day we arrived in Pamplona, and the day we left. Then things improved. Until the day we walked into Santiago, its was sunny every day except for one shower as we arrived in Sahagun. Most days were 18-24, with chilly +6 C mornings on the meseta, +10 C mornings elsewhere. On my third, it was the Norte, but arrived in Galicia in a May heat wave. +30's for three days.
I suspect you are really asking what to pack. You needs shorts and a short sleeve for the nice days, and a wide brim sun hat. Hope you need it! You also need a warmer long sleeve, a fleece hoody, and a rain jacket. On the cold days, you wear everything in your pack. Wearing everything, you need to be comfortable at 0C in a moderate wind. Piece of cake for a 'pegger. Its all about layers....3-5 layers with an empty backpack when you set off on a cold morning, with each peeling off as the day warms up until you finish the day, often in shorts and a T-shirt.
The climate is temperate, but the weather is day-to day and year-to-year. Prepare for it all. As for Albergues, everything opens Easter week, so make sure you know when that is. Before then, there are a few places that will be closed, but not many, and finding a place on the Frances will not be an issue.
Buen Camino