Whisk together the vinegar and dry mustard powder in a nonreactive bowl. Cover the mixture and let it sit overnight.

In a small pot, combine the mustard mixture, sugar, and egg and whisk to combine. Place the pot over medium heat and cook until the mixture reaches 165°F, using a candy thermometer to monitor the temperature. Hold the mixture at 165°F for a few minutes, adjusting the heat as necessary. Remove the pot from the heat.

Store the sweet hot mustard in an airtight container in the refrigerator for up to 4 weeks.