But water does more damage when the weather is cool and damp and evaporation is not available.
of course you should fix this ASAP. I am not downplaying any water leaking on untreated wood. I would be more concerned about insulation and Tyvek being compromised.
It would be very wise to fix this problem very quickly and do any thing you can to ventilate the area in question.
Until its fixed, I would so something with a tarp or building paper or caulk to prevent more water leaking before heavy rains or rains in general.
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