by bluenote23
Look at the rulebook, page 17.So put the 4 tokens in the space. If an investigator leaves that space, then you put a different fire token on their dashboard. The number of fire tokens in spaces is limited to the 12 available in the game. The number of fire tokens that can be on a dashboard is unlimited.
So if you have used all the fire tokens by putting them on spaces and on players' dashboards and then you have to put more fire tokens in spaces, then you need to proxy the tokens on the dashboards and use them for the space.
This assumes that in your original question, the wording is specifically "spaces".