Whisk remaining 1/4 cup sugar and egg whites in a heatproof mixer bowl set over (not in) a pan of simmering water. Whisk until sugar is dissolved and mixture is warm (it should feel smooth between your fingers), 2 to 3 minutes. (For fully cooked eggs, a thermometer inserted into meringue should register 160 degrees.) Remove from heat. With a mixer on high speed, beat until stiff peaks form, about 5 minutes. Fold into eggnog.