In reply to Superterence:
Likely not too hot, though I suppose there could be a heatwave. I've done it in May and in December and can't remember noticing much more or less comfort either time. We find by far the most economical way of "doing" Costa Blanca" is to rent an apartment - very very cheap outside the holiday season. Calpe's the favourite destination but any of the towns along the coast will do.
In May you should get an apartment for 4 people for under £50 per head. In December we usually manage a week for 4 including flight, car parking at UK airport, car hire, fuel, and apartment rental for under £200 per person. Eating out is varied and cheap. I generally do the bookings through
http://www.lowcostholidays.com or
https://www.travelrepublic.co.uk/ who's websites let you pick your flight and apartment and do the rest for you. All very easily done.
Unless, that is, you insist on rural charm and the bucolic way of life of the hinterland villages, in which case not so cheap or simple to arrange, but websites like
https://www.homeaway.co.uk/ and
https://www.airbnb.co.uk/ are good for private apartment or villa rentals.