The TAG safari shirts (availabe in Zim and online via Texas) and the Salty (Zim) shirts are cotton and much more breathable than the other options. The older cabelas safari shirts (usually green or tan with the shoulder patch) were iron tough but they were so damned hot. The Orvis Bush Shirts are very durable but also crazy thick.
For comfort, I really like the African made bush shirts as they are cheap and cool. Going another route, the modern merino wool t-shirts in the USA are also the right colors and very cool and low-odor. (first lite, sitka, kuiu, icebreaker)
Another very, very good bush shirt that is highly collectible and no longer made are the Willis & Geiger ones. You can find them on ebay. Some days they are $35, other days they go for $300. They were the world's finest, good enough for Edmond Hillary and Ernest Hemmingway.
Postscript: to answer your question about hot irons, ALL of these can take a hot iron in Africa without damage.