Don't think most plastic straws would melt, but they would probably soften and might infuse more chemicals into your beverage than it would if it were cold. At this point I'd just go for the obvious solution of repurposing an old heat exchanger from an AC unit or something. The strange taste will go away after a few times (probably).
Yeah, I won't drink anything hot out of plastic anymore: Corpos lied to us for decades that it was safe but it wasn't and now we're full of all sorts of terrible shit. The straw probably wouldn't deform, but it probably would leech all sorts of chemicals into the water.