The phrase "burn with curiosity" is often used to describe an intense desire to know or learn about something. However, using the same phrase repeatedly can become repetitive and boring. Fortunately, there are several alternative ways to express this idea using other words and phrases. Some examples include "fueled by an insatiable thirst for knowledge," "consumed with a passionate drive to uncover the truth," "consuming desire to explore," "aching to unravel the mysteries," and "yearning to satisfy an insatiable curiosity." By incorporating these synonyms into your writing, you can add variety and interest to your work while still conveying the same message.