PREVENTING FROZEN PIPES

Measure the actual basement tempurature. I am thinking the frost may not get that deep.

Otherwise I would recommend one of the propane catalytic heaters with O2 and CO sensors in place.
Should have IMO a CO sensor upstairs anyway with a fire going 24/7.

If her basement is mostly underground and the upstairs is above freezing there should not be any frozen pipes. Unless the basement is not sealed up well and cold air is blowing on a pipe someplace.

wgriswold's got it. Crack the faucets, and let them dribble. Open the cabinet doors under the sinks, and let whatever little bit of warm air might be in the house into the space where the pipes are.

Alternatively, look if there is a shutoff valve & drain where the water comes into the house. Shut off the main valve, then open the drain (have a bucket handy!). Open all the faucets, and drain all the water you can out of the house lines.

Then cross your fingers. How cold is it supposed to get at night?

Kerosene heater inside an enclosed space requires ventilation if I am not mistaken...which in my eyes defeats the purpose (unless I am wrong here)

Kerosene heater?

Turn the faucets on. More flow through the cold than the hot.