Albert Barnes Commentary 2 Chronicles 29:31

"Then Hezekiah answered and said, Now ye have consecrated yourselves unto Jehovah; come near and bring sacrifices and thank-offerings into the house of Jehovah. And the assembly brought in sacrifices and thank-offerings; and as many as were of a willing heart [brought] burnt-offerings." — 2 Chronicles 29:31 (ASV)

Hezekiah addresses, not the priests, but the congregation: “Now that by the atoning sacrifice which has been offered for you, you are consecrated once more to be a holy people to the Lord, approach with confidence and offer your free-will offerings as of old.”

Burnt offerings—The term translated this way applies especially to those victims that were to be wholly consumed upon the altar. In the “sacrifices,” or peace offerings generally, and the “thank offerings”—a particular kind of peace offering (Leviticus 7:12)—the greater part of the victim belonged to, and was consumed by, the worshipper. Hence, to offer “burnt offerings” was indicative of a “free heart.”