What you are referring to is Florida Statute 83.51. This statute, among other things, contains a provision which provides for the landlord to make "reasonable provisions" for "functioning facilities for heat during winter." First of all, this provision may be varied by the terms of your lease, so you should review that document to see if it specifically allows a space heater. In addition, if you are renting a single family home or duplex, this provision does not apply. Now, for the fundamental part of your question. Whether a space heater is a "functioning facility" or provides a "reasonable provision" for heat is not clearly specified in the statute and could be open to interpretation.
If the property does not have central air conditioning or heat, then such a unit may be a reasonable provision and acceptable under the lease. If the property does have central air and heat, but same is no longer working and the landlord has refused to repair same (and has an obligation under the lease to do so), then it is very possible that a space heater is not acceptable.
This information is intended to give you some basic thoughts and guidelines only since there is no clear statutory guidance regarding space heaters. I would suggest you consider consulting with a real estate attorney to review the particular circumstances of your situation including the lease agreement that you have with your current landlord if you are still uncertain.