Yes, I do realize the way to stay warm in the pool is to swim harder. 😉 However, if you're one of us “adult onset swimmers” that does classes where there's a lot of drilling and standing for instruction and/or you’re a very lean athlete, the pool can get pretty darn cold.
After watching one of my teammates shiver through a workout, I lent her the gear I bought for my Total Immersion class. I had purchased an insulated long sleeve top for that class because I was afraid I’d freeze to death with two days of swim instruction in and out of the pool. (This coming from a person who has fingers that go white and numb at the first hint of cold.)
Thankfully, that class turned out to be well structured with a lot of classroom work first, and in between pool sessions there was a chance to shower and change into warm clothes. Between the structure of the class and the long top, I was comfortable the whole time despite my initial concerns. And since the top helped my teammate in class, too, here’s some info on where to buy similar swim tops for my fellow shivering triathlon swim training friends!
DAKINE Neo Insulator Rashguard - Long-Sleeve - Women’s
While this specific model is discontinued, there are other insulated rashguards on the market, which is ultimately what you’re looking for. They seem to be marketed most at surfers, so that’s something else to consider in your search. I picked up this model at backcountry.com, a great place to get high quality gear at good prices. For a special backcountry code, see the discounts page. (BTW - The short sleeve version is still on closeout at some places, and would probably work as it's the insulated core that's probably doing the most work to keep you warm.)
I've also picked up light-weight long sleeve swim tops at Land's End for outdoor swimming (sun protection in that case!). I see some people use them for water areobics as well, so they might be just enough extra insulation to work for a tri swim class, too.
Specs on the above Long Sleeve Half-Zip Rash Guard from Land's End:
In summary, you're looking for rash guards which are typically non-insulated, and might be considered surfing gear. Select a verison with an insulated/neoprene core for more warmth. And if you've got a favorite I haven't mentioned here, would love to hear about it in the comments!