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I try to provide a general-applicable answer to this broad questions:
From April to November you will have the widest selection of cruise ships. End of October the holiday season in Europe comes to an end and a lot of small cruise lines and tourist locations in the whole Mediterranean sea just shut down. Note that a few cruise lines operate in the Mediterranean year round. So cruise ships will be available nevertheless during the winter. From June to August it is the high season. Prices are the highest then.
The temperatures during the summer can really be very hot. It is not uncommon to reach almost 40 degrees even on the ocean. On the other hand, in winter the temperatures are sometimes so low that you can go outside without a jacket and you can't really enjoy the sea. So the best time based on the temperatures is in the spring and autumn.