I would recommend they bring the entire closet to 'current code standards, which typically include a ceiling and combustion make up air vents' and let the contractor figure out what that 'current code' is.

This way, you've made the recommendation to install a ceiling, and 'reminded' the contractor about combustion make up air, then advised 'current code', which will kick in all the other things required too, insulation, etc.

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Jerry Peck, Construction / Litigation Consultant
Construction Litigation Consultants, LLC ( www.ConstructionLitigationConsultants.com )