You will also find many bars and restaurants closed as locals leave the cities and head for the beach. I am a frequent visitor to Seville and Spain in general, but never go in July or August. If you visit the coastal areas at this time it will be extremely busy.
To answer your question, yes it's high season for airlines. High season in Spain and Portugal do not directly play into the price of your flight. It's the reduction in the number of seats available on all international flight and the price of fuel (oil).
As already noted, it will be very warm in late July in Madrid, early July in Sevilla. It's mild right now in Lisbon, but it will be on the warm side in July. You might want to consider heading for the north coast, anywhere from Galicia to the Basque country (more like the Bay area), where it should be a bit milder unless Global Warming gets really freaky.
I actually just heard on NPR yesterday (US National Public Radio) that airfares are expected to continue to rise over the next few weeks and months and that this summer they will be especially high. Summer is peak season for Europe (think schools/universities out on break, family travel, summer learning etc). If you can afford these prices now it was recommended you buy soon rather than wait on the prices of tickets, as they are expected to continue to rise.
In the US, try kayak.com for fare comparison as momondo.com usually does not give a fare that includes taxes etc (it's usually a bait and switch fare, very low but then you can't get it). Also I like booking.com for hotels in Europe.
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