Safety-wise, it’s not really any different from an incandescent or halogen bulb at the same wattage. Presumably she’s old enough to remember when there were 60-100 watt bulbs in all kinds of old fixtures all over the house? I mean, you wouldn’t turn on a 100-watt light bulb and leave it lying around on a pile of oil-soaked newspaper.
If she’s still nervous, get a radiant heat panel. They’re sort of expensive, but way cheaper than cranking up the heat in the whole house for the whole winter, and they are designed to run at temperatures low enough that you can safely touch them. You can buy a fair amount of expensive heating equipment for less than the cost of heating your whole house or a large part of your house instead.