I agree with Pete. The chances of you finding work for a 3 month period are slim. Schools in Seville, where I have been working for the past 5 years, begin the school term in October and end in June.
The only likely source of employment is going to be relief teaching for sickness. Try contacting some of the schools well in advance.
You also need to be aware of the need for a NIE - the national identification number - without which you will not be able to do any work. It can take hours of queueing and weeks of waiting before you get one of these.
Then there is the question of accommodation. If you arrive in Seville in March you arrive when the Semana Santa, the Feria, and various other festivals are starting. The availability of accommodation at these times is more problematic. In the past few years, Seville, like most European cities, has seen a huge rise in the cost of a room. Expect to pay 150-350 a month for a small room in a shared flat.
The only other alternative is to teach privately, but it takes time to advertise and find students. Without savings available you will soon run out of money.
As for Seville, it really is one of the most amazing and beautiful cities in Europe. It's forever warm and there is always plenty going on. It is a great place to teach, and many teacher who come here for "a year" end up staying forever. If you are serious about teaching in Seville, you need to start applying to schools in July-August, and plan to arrive in September to get the necessary accommodation and documentation sorted out before starting work.
Why don't you come over for a couple of weeks - you sound as if you could afford that - get a feel for the place and visit some of the many language schools?