"With burning cheeks" is a common phrase used to describe someone who is experiencing embarrassment, anger, or any strong emotion that might result in a reddening of their face. However, there are several synonyms for this phrase that can be used to convey similar emotions, such as "flushed face," "red-faced," or "blushing." Other options include "heated cheeks," "rosy complexion," or simply "flushed." These alternatives can add more variety to your writing or speaking, and can help you avoid overusing the same words or phrases multiple times, while still conveying the same message.