There is the striped ticking uniform (frock and trousers) which belonged to Pvt. Schumpert (3rd South Carolina Inf.), but its origins are in question - unless someone else has more info - and the type seems to be limited to the western theater.
If it is that much of an issue, how about a lighter weight jean cloth, there seems to be quite a variety in original garments and available modern material.
"Why, it's just like shooting squirrels, only these squirrels have guns, that's all."
Pvt. A.C. Varis, 17th Illinois, at Shiloh