Space heaters are such a hazard. Babies throw things into the most unlikely places, and one of them would eventually be the heater. Especially if it's red (hot) or has a moving part (fan).
I'd go with shakran's zoning. You'll need valves and at least one more stat/sender, but it would be the most convenient. The other side would be investing in window covering and insulation.
Maybe put the baby in the most central room that stays warm the longest, even if just for the winter.
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There are a vast number of people who are uninformed and heavily propagandized, but fundamentally decent. The propaganda that inundates them is effective when unchallenged, but much of it goes only skin deep. If they can be brought to raise questions and apply their decent instincts and basic intelligence, many people quickly escape the confines of the doctrinal system and are willing to do something to help others who are really suffering and oppressed." -Manufacturing Consent: Noam Chomsky and the Media, p. 195
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