Mine often show through polo shirts. One of my less couth coworkers pointed it out. People just have to learn to deal with it. It’s too hot here 10-11 months out of the year to consider a second layer of clothing. Besides, if folks are looking at my chest, it’s because of the pecs, not the nips.
If nipples showing are the only concern, you can get away with a tank-top style T-shirt, which will at least be a bit cooler than one with sleeves. Me, I have to wear a short-sleeve tee, because my shoulder tattoo is visible through certain dress shirts. Bummer.
I always wear a t-shirt under my shirt-shirt and I’ve done this since I was in the Army and it was a part of the uniform. I wash the t-shirts after every wearing but I wear the shirt-shirt a couple/few times before washing them. In theory, this may make them last longer.
The occasional accidental appearance, I would say no. It would be poor etiquette to wear a shirt with holes cut to make them clearly viable, tho … 
Now that I understand the question a bit better, I am slightly more confused. Do you, in the course of your duties, move between different climates a lot? For instance, a car salesman who spends time both on the lot and in the showroom? Or a manager both in the office and in the warehouse or factory?
Because if you are cold enough that your nipples are all perky, you probably aren’t wearing a warm enough shirt. And if wearing a warmer shirt or an undershirt would make you sweat, then I don’t think you are getting cold enough for nipple pop-o-matic action.
So the only way I see this being an issue is if you are trying to find a shirt that won’t make you sweat too much when you are somewhere hot, but won’t show your studdly sweater-bumpers when you get hit with a blast of cold air.
Which is enough of a challenge that I think your co-workers will just have to learn to suck it up and try their best not to be overcome by your attractiveness.
Why should girls have all the fun?
viable, not viable.
And another witty comment is killed by Lord Typo.
sigh.
Pasties. Won’t bulk you up or make you sweat. And they come in so many designs! Or for the budget-minded, there’s approximately a billion tutorials online to make your own. (Blinking lights and tassels are optional, but highly encouraged.)
It’s a double homicide.
And if they don’t, you’re doing it wrong.