Certainly you can try to pasteurize (heat at a certain temperature for a certain amount of time) your wine if you like. Many foods and beverages (like milk) are so heat treated in order to kill any bacteria, yeast or other organisms. Louis Pasteur, the Frenchman who gave the process his name back in the 1800s, actually was hired by a winery to research methods to increase the stability of wine and to keep it from turning to vinegar. Typical pasteurization for milk involves heating it to 161 °F (72 °C) and holding it at that temperature for 15 seconds, then rapidly cooling it down back to 45 °F (7 °C) or so. I would caution that at that high of a temperature because the higher the temperature, the more damage you will do to the delicate aromas, colors and flavors in the wine.
Fortunately, pasteurization operates on a sliding scale and its effectiveness depends on a coefficient between time and temperature. You can use lower temperatures (145 °F/63 °C for example) but you must hold the wine at that temperature for a longer time, or about 30 minutes. This is what’s known as “batch pasteurization” or “vat pasteurization”. To do this, you’ll need a big pot that will hold bottles of your wine completely submerged, as well as a thermometer. A nice digital one with a probe on a cord, and a large readout would be ideal. You might have a problem finding a vessel big enough as your average kitchen pasta pan probably will be too small. One container I know would work is my grandma’s big turkey roasting pan, which is long enough to span two burners and tall enough to hold a single layer of wine bottles.
Fill your kitchen sink with cold water and toss in two handfuls of ice cubes. The goal is to have cold water, not ice water. Fill your big pan with enough water so that when you add the bottles, they are completely submerged. Heat the water to about 150 °F (66 °C), and carefully slip the bottles in. Keep the heat source on low/medium such that the temperature hovers around 145 °F (63 °C). Expect the water temperature to go down as your cooler bottles acclimate to the water bath. Hold at 145 °F (63 °C) for 30 minutes using the digital timer. After 30 minutes, remove the bottles (a canning jar lifter and hot pads might be useful) then lay them down in the sink in the cold water bath to rapidly chill. Repeat the above for as many bottles of wine as you would like to heat treat, adding ice to your sink as necessary and always making sure your water bath is at 145 °F (63 °C) for a full 30 minutes. Be careful when transferring hot bottles into cold water as the glass can very easily break with just a tap.
As pasteurizing wine is a big chore (as you can read above) and as it can negatively impact the character of one’s wine (even at lower temperatures and longer times) I always recommend that people speak with their physician to truly diagnose a sulfite allergy, which only affects a small fraction of the population. If you truly are allergic to sulfites, you should be aware that all wines (in fact all fermented beverages) will contain a small amount of naturally-occurring sulfites and that there is no such thing as a completely sulfite-free wine. Pasteurization should help in keeping your wine shelf stable due to microbial spoilage for quite a while though it could be argued you could get a similar effect using good sanitation and sterile filtering your wine before bottling. Unfortunately, pasteurization will not prevent oxidation in the bottle and if you don’t add sulfites, even to pasteurized wine, you will definitely notice that the wines won’t age as well or as gracefully as if you had added sulfites. If you can handle low levels of sulfites you might try a combination of sterile filtration, pasteurization and bottling with 10–15 ppm Free SO2, which is much lower than the standard 25–30 ppm. This would build in some protection against microbes (the filtration and pasteurization) while helping provide some antioxidant protection for graceful aging.