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Oil stoves - heaters burning paraffin - were even more portable than electric fires because they didn't need an electric socket. Furthermore paraffin oil was relatively cheap.
That, though, was where the advantages ended. Paraffin heaters supplied only background heat, and burnt with a naked flame that was a serious fire-risk if the stove was knocked over and the paraffin was spilt. Also, as the stove didn't have a chimney, the burning produced a great deal of condensation, and it smelt badly. I think everyone would have felt ill if they stayed for long in the environment of an old oil heater.
In the 1950s we had a paraffin heater in the shape of a radiator. At the time, I thought this most luxurious as the homes of ordinary people did not have central heating.
In our bathroom we had a paraffin heater which we used to light for about 10 minutes before starting to run a bath, and it would stay lit - unvented - until the last bath was finished. How we never succumbed to carbon-monoxide poisoning is a complete mystery to me in retrospect, but we didn't know it was dangerous back then!
If you have an old photo which would illustrate the way of life described here, I would very much appreciate a copy.