Winter has a way of pulling every warm object into one corner of the house. A space heater by his chair, an electric blanket, a lamp on the same power strip. You may find them all plugged in at once, and you may find him cold in the hallway because the furnace cannot keep up with rooms he is not using much. Both things are true. The fix is not to take the heater away from him.
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Look at the outlet, then the cord
Start at the wall. Feel the outlet plate and the plug. Look for browned or darkened edges, a faint burnt smell, plugs that wobble, or a plate that is warm when nothing has been running for long. Then follow the cord. A cord under a rug or a runner cannot shed heat. Move the heater onto a hard, flat floor with clear space around it, away from curtains and the arm of the chair.
Count what shares the circuit
Ask which other things share that outlet or power strip. A heater on a strip with a lamp, a clock radio, and a second heater is asking the outlet for more than it can safely give. Plug the heater straight into the wall where you can, and do not run it from an extension cord unless the heater's own instructions allow it.
Watch for signs it is working too hard
A breaker that trips in the same room more than once, lights that dim when the heater cycles on, or a cord that is warm to the touch are all reasons to stop using that outlet and call an electrician. Do not wait until the next cold night to decide.
Set a few rules he can live with
Ask him to turn the heater off when he leaves the chair, and to keep it off overnight unless the room truly turns cold. Show him the switch, the tip-over shutoff if it has one, and where the cord rests. Make it a shared rule, not a lecture. Tie the check to something he already does every evening, like the news or his last cup of tea.