A cotton-navy blazer would certainly be weather/temperature appropriate, however, it certainly depends on the blazer itself. The problem with cotton, especially darker colors of cotton, is that it tends to show “wear” after a while in use (ie: dark denim getting lighter in color after multiple wears). Some cotton sport coats and blazers come pre-distressed and quite a bit faded. For a more professional setting, this can not look as great.
As an alternative to cotton, I’d suggest linen. The downside to linen is that it’s very prone to wrinkling (in fact, it’s outright guaranteed). You could also look for a linen-cotton blended jacket, which would be somewhat more wrinkle-resistant.
A final alternative would be tropical wool. This would be very lightweight, be very wrinkle resistant and much more professional in appearance than cotton or linen.
Regardless of what jacket you choose to get, make sure you get one that’s either unlined or partially lined. Full lining will make you sweat. The best lining option would be where the sleeves are lined and only the upper shoulder area. This will allow you to put on your jacket with great ease while minimizing the heat retention and breathability.
ADDING: I should note that patch pockets are more casual/sport-ish than flap welt pockets in a blazer, even more so if the breast pocket is a patch pocket. If you want to be more formal, then go for a tropical wool blazer with welt/flap pockets or patch pockets with a flap and a welt breast pocket. Ideally, this would also include metal buttons. Still, I think you could go more casually in a lot of office workplaces these days and get away with something less formal (and more casual) and still be better dressed than 90% of the people at work.
Hope this helps!