Screens get treated as an afterthought, which is strange given what they do here. A sun screen is the only intervention that stops solar energy on the outside of the building, and stopping it outside is meaningfully more effective than managing it once it has already come through the glass and landed on your floor.
If you have one room on the west side that runs several degrees hotter than the rest of the house no matter what the thermostat says, screens are usually the first thing worth trying and the least expensive.
A sun screen is a dense woven mesh in an exterior frame, mounted over the opening. Depending on the weave density it blocks a substantial share of solar energy, and it does that work in open air where the absorbed heat blows off rather than radiating into the room.
There is a second benefit that most people never hear about. By shading the pane, a sun screen lowers the peak surface temperature of the glass, and peak surface temperature is what drives the daily thermal cycling that eventually kills the seal on a dual pane unit. Screens on a west elevation are quietly extending the life of the windows behind them.
Standard mesh for keeping bugs out while a window is open, which in Mesa also means keeping a fair amount of dust out. These are lighter, more transparent, and not designed to block solar energy in any serious way. Different job, different mesh.
West and south elevations, without much question. Those are the walls taking the afternoon load, and afternoon is when the heat compounds because the structure has been absorbing energy all day. North-facing windows get comparatively little direct sun, and screening them costs you daylight for very little thermal return.
Screening the two or three worst windows in the house usually delivers most of the comfort gain for a fraction of the cost of doing every opening. Start with the room you already avoid in the afternoon.
If the frames are still straight and it is only the mesh that has gone brittle, torn or sagged, rescreening is cheaper than new screens. Sun exposure degrades mesh over time regardless of quality, so this is normal maintenance rather than a sign anything was wrong.
Screens are made to the opening rather than trimmed from stock, which matters on older Mesa homes where openings vary. A screen that does not sit properly in the channel will rattle, let insects past the gap, and work loose in monsoon wind.
Tell us which windows are causing the trouble and we will measure them and price the screens at no cost.