You need to keep the sun off the home in the first place. Okay lighter render or paint would be good, but the wall will still heat up and windows will still get lots of sun. You have to actually have a barrier before the wall or windows. So yes a trellis with vines would work, but it would need maintenance all year round. Have you looked at fence to roof screens. You can still have plants to add greenery, but not a vine.

https://allaboutshade.com.au/outdoor-blinds/roof-to-fence/?gclid=EAIaIQobChMI8pvws9rG9QIVW5hmAh2CBg7fEAAYASAAEgJdpPD_BwE

Plants also need maintenance. They can be very effective but need good planning. Structure adequate to support the weight, watering, choice of plants for the orientation and conditions, and even when you think you've done all that they don't always grow well and evenly, or they grow too well and need frequent pruning .

My first thought was shadecloth too.

I think part of the cooling effect with plants is transpiration, which you don't get with shadecloth, so maybe both?

Shade cloth a good idea, thanks, but may not work for our western wall as it's 2 storeys and around 1.5m from property boundary.

Great suggestions and advice from dreamer and macyjean, you could try decorative screens to add dappled shade, battens look great, star jasmine looks wonderful and smells divine or a simple structure with shade cloth will cut down on the heat

A double storey home with a western sun side is a different scenario altogether. Good to have full information.
Make sure if building this home, you have eaves on the top storey roof. This will help shade some of the upper wall. Then any structure you build on a 1500mm boundary may need council permission. Shade cloth from house to fence is still possible, but would need more work to drill into brick walls. Also install external shade awnings or horizontal slats on any windows on upper storey. Hopefully you don’t have many. As said it is making sure the sun does not get to the windows in the first place. Light bricks or render also.

I have these luxaflex aluminium external louvre on my upstairs bathroom window. They do make a huge difference. Mine are fixed blades.

Another example

Do you have wall insulation?

What rooms have windows on that side, do you need some light during the day but reduced heat, or is it alright for those rooms to be dark?

Just as a note, the link I added to my earlier post gives details of spans. x 1500mm to fence is doable.

This is my upstairs bathroom just now, it has been a 41 degree Celsius day in Perth today. It is very light room no issues at all with being dark. The bathroom is good. Before the luxaflex horizontal louvers were installed my children’s toothpaste was literally melting. I realised this on the first summer in this home. Even though it is on the south west corner, it still gets way too much sun at this time of year.

These are all great suggestions, thankyou. There is one window on the western wall that is already shaded with a wind up/down awning. It's the large expanse of brick that I am concerned with, thinking that if I can stop the sun soaking into the brick then maybe our house won't get so hot. We have insulated the roof, added awnings to all north and west windows, and added a solar powered whirly bird to take heat out of roof space, but it's just a hot house. Unfortunately my neighbour does not like trees so I can't encourage him to plant on his property to help shade our place or his! Our next step is to replace some of the windows with some that allow better cross ventilation.

i wonder if adding insulated cladding over the bricks to create an air gap as well as shading the windows would be the best long term solution and may not be any more expensive than render

Is the western wall insulated? Speaking from experience it makes a big difference. When you say you have insulated the roof it sounds as if you did that after the house was built? So if it was not already insulated perhaps there is no wall insulation either?

As suggested stopping the sun hitting the wall is the best solution. Then insulation. Forget render. Pull off the gyprock/plaster from inside (it’s much cheaper than render) and add insulation. It will be inconvenient but will give you a good outcome.

Yes I agree, is your house insulated, is it double brick or brick veneer? If double brick there should of been a insulation membrane installed between bricks when built. If brick veneer there should be insulation in the studs. I would check that out.