Rags to Riches with Seasons

Rags to Riches is my go to playstyle too. The only solution I can think of that might work depends on the conditions required to prevent heatstroke. Do you need to escape the heat or only the Sun? If you don't have to physically be inside four walls with a roof overhead, and some kind of cooling system (like AC, a pool, etc.) but just under some kind of roof (like vampires), put a roof up over your Sim's campsite.

Rooves are free and instantly available. Sure, it would have to float until you can afford some walls or columns, and it's not very realistic if that's your style too, but it would be an effective way to get out of the sun. :)

I also wonder if taking a cool shower would be effective? In that case perhaps one of those tarp showers would work to keep cool? Just a thought...

EDIT: Also, the Toddler SP came with those freestanding tarp dealios for shade. If you have that pack, it might be more realistic looking for a homeless person to use that instead of a floating roof. Again, I'm going on the assumption you just need to get away from the Sun. If you need something to cool off as well, perhaps using the tarp shade and tarp shower together would work. *shrugs*