You might like a pasta strainer that fits inside the pot. When the pasta is cooked you lift the strainer out of the pot and leave the pot of hot water sitting on the stove or in the sink. There's still some steam exposure but not nearly as much. You can re-use the hot water (for a second batch of pasta, soup, hot chocolate, etc), or let it sit in the pot until it's cool enough to pour out conveniently.
There are pot/strainer combo sets like the example below, or you can get a separate strainer insert that fits a pot you already have.
The small downside (aside from purchasing and storing an extra strainer) is that the strainer inserts tend not to have as tall a "foot" as a stand-alone pasta strainer. So you won't want to set the strainer down in the sink because the pasta might come in contact with the surface of the sink (which presumably is not clean enough to eat off of, unless your sink is cleaner or your "ick" threshold is higher than mine). The solution is to have a bowl sitting by ready to pour the pasta into it. Then you can put the strainer back in the pot.