In my experience it can remain chilly at night and higher chance of rain until late April/early May. Starts to really heat up in June and July and August usually hot but varies from year to year, with 'cooler' and then hotter summers. It starts to cool down again in September.

May is a lovely month but remember the sea has not warmed up by then and the municipal swimming pool;s will not be open. It is a good time for lovely spring flowers and still nice and green with the cherries ripening in May.

September and October and generally warm but the days are shortening and there can be rain, torrential at that!. The sea will still be lovely and warm and you can sunbathe on many days during these months. November can have some great days but is becoming less reliable and can be windy and cool.

You mention the temperatures but it is worth pointing out that generally by February in Catalunya you will enjoy some spring like, sunny days. Even if it freezes at night it generally thaws very quickly if the sun is out and by midday can be warm again.

If it is your first visit and you don't mind a cold sea I would recommend May, it is a lovely month for getting out and enjoying the beauty of the area.

Have a great time!