Excuse my duh-ness but i'm having difficulty trying to follow whats going on here. Are these two photos an exact replica of your house and pool ? If not a hasty sketch with dimensions could help a lot. By kitchen wall do you mean the wall behind the bar ? And where is the pool wall ? Are you considering the covered area as being "inside" ? Sorry for all those questions lol Sometimes when you have a design problem you need to turn it inside out or on it's head. If you can't beat it maybe embrace it by making a feature of it : i.e. contrast by having the lightest colored pool surround and a great blue or tile inside and under the overhang, something that will echo the water color ? If you have a great covered area as in photo you'll most likely be spending a lot of time there and it could be soothing to be able to sometimes retire into a darker inside. In my book, 10M isn't small and also contrasting two floor colors doesn't necessarily make a space seem smaller and confined and may in fact even open it up. Could it be that you've thought yourself into a box here ? Sometimes one needs to give it all a good shake up and see how it resettles.

If you are seeking a truly open feel to the floor plan you have shared, then using one material in the mail living area is the best approach to making this space feel truly open. Using a variety of materials on flooring chops up the space and decreases the visual footprint. I would suggest using wood, tile, or if you are on a tight budget laminated flooring for the living/dining/kitchen. Then use carpet in the more intimate spaces; bedrooms and possibly hallway. Save the tile for the bathrooms.

I recently saw this episode of Ask This Old House where they demonstrated painting tiles - especially as a solution to get one through till an entire redo is possible. http://www.thisoldhouse.com/toh/tv/ask-toh/video/0,,20902001,00.html Looks like you are doing a great job!

I cant imagine that tiles on concrete will be any colder than concrete alone. But the choice of colour may make a difference to the heat absorption qualities; dark tiles will absorb heat better than light coloured ones.