I doubt it is possible. When the server is running it will need to be ventilated, unless you build a refrigeration unit into the cabinet. You will need an automatic graceful close-down of your system rather than letting it crash when the power goes.
Fire-proof safes get quite hot inside, they delay the contents heating up. It is easier to protect papers from getting hot enough to burn, than to prevent hard disks getting hot enough to be damaged. You can buy second-hand firesafes quite cheaply, because they are large and heavy and difficult to move.
A fire-protected machine room will probably have walls, floor, ceiling and doors give at least an hour of additional protection, and a gas-extinguishing system, backed up with a scram alarm to make everybody get out of the room before they are suffocated. It then relies on the fire brigade arriving quickly enough to stop the building collapsing. In some cases concrete bunkers are used, which may be underground.
Having worked in the biz, I recommend that you use the offsite storage approach. Either put your data in the cloud, or put a back-up file server in a brick shed at the bottom of the garden, so that if your house burns down, the shed will probably still be standing.
