I've never trellised malabar spinach (I use it in cooking too often to reach that point) but in my experience, malabar spinach loves the heat. In fact the hotter it is, the faster it grows. It is a tropical plant so I would be really surprised to learn that it wouldn't thrive under those conditions.

I have grown it while living in New Orleans. Think sauna. I had mine on a pergola so it did get some self made shade and was not against a brick wall. Even when it becomes a very long vine the leaves are tender and tasty.
Mike

Very heat tolerant. Mine thrived in south Florida summers - climbed up over the top of an orange tree where it got pretty much full sun. It was mostly in containers, so even the roots would get pretty hot there on the patio.

I recommend regularly harvesting the tender tips rather than letting it get tall. Vigorous self-seeder.