A purpose built fireproof safe is supposed to 'fail' closed. Those Sentry or whomever you buy in the store. They are a plastic on the outside that is designed to melt therefore sealing the gap where the lid opens to prevent water intrusion.
My gun safe has special rubber seals around the door that are supposed to melt sealing the door from water/smoke intrusion as well.

The thing to be careful of if you put your documents in a baggie is the safe is only heat resistant, it won't prevent it from getting hot inside, what its designed to do is keep the inside temperatures from reaching the flashpoint of paper. The melting point of most plastics is below the flashpoint of paper so plastic in your fire safe can melt even though the paper is safe. Thats why they make media safe's that cost more but keep a lower internal temperature below where your plastic cd's and such will melt.

I found that by the time you pay $200 or more for a media fire safe I paid $500 for a gun safe which had an even better fire rating than the media safe and the cost per square inch was much lower. Gave us an excuse to drive to Cabelas too as they had them in stock so no $hipping charges.