If you need a thicker syrup (for candy, pâte à bombe, or Italian meringue), keep heating without stirring.
Use a candy thermometer to monitor temperature:
Soft-ball stage: 235–240°F (112–116°C)
Firm-ball stage: 245–250°F (118–121°C)
Hard-crack stage: 300–310°F (149–154°C)