I wouldn't consider renting a property with those terms and conditions. It costs between $3 & $5 a day just to run the pool pump to keep the water circulating through the filter with no heating!
We own a villa in Spain and it's quite common for owners to add an extra weekly charge for central heating in the winter months. However, it tends to be a set fee and is not open ended like this is.
I would take Sandra's advice and have a look at the villas listed on the sites accessible through the links at the top of this forum.
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