I would not consider this "pasteurization," which has a specific meaning in food science, but the method of "cooking" sugar to around 240°F or 116°C and threading it into an egg foam is an accepted and proved method of ensuring the food safety in your meringue. You do not need to check the temperature, but you can feel the mixing bowl (especially if it's metal) and you'll get an idea of how hot it is and how long it takes to cool to room temp.
As a side note, I would not employ the method you state exactly. I find it's best to use about 1/3 of the sugar uncooked and add it to the eggs (French meringue-style) after it has reached soft peaks (or at least a decent foam, depending on your sugar grain size) and then beat the whites to a a medium peak before threading in your sugar. There are many methods that work well, so if the recipe you're following works for you then that's great as well.
You can also add an acid (like cream of tartar) to the whites before beating them which helps prevent the proteins from bonding too tightly and also helps the foam form.
If you're very concerned with food safety another method you can use is the Swiss method where you cook the egg whites and sugar over a double-boiler first (to 160°F or 70°C) and then beat them in your stand mixer with the whisk. I prefer the Italian method, but this works well and is easier to do.