keeping an empty house at 49F during the winter: heat pump or radiant oil heater?

I have a house in southern Oregon. I am not there much in the winter, and this past February, I was surprised to get an electricity bill that was double the usual bill. I keep the thermostat at the house at 49F, and there's a heat pump. Normally the electricity bill is about $60, and the February bill was $130. I am pretty sure that the reason for the relatively high electricity bill was due to just three days of temperatures at 0F. The lows were between 21F to 32F all month otherwise.

I am pretty sure that my heat pump was struggling to keep the house at 49F during those three cold days. I believe that when the heat pump struggles with low temps, it may turn on EM (emergency) heating. A friend suggested that I buy a radiant oil heater with a built-in thermostat. He wrote: "For your winter heat, I'd use a radiant oil heater. They work great for this kind of thing, and they even have a built-in thermostat. You can plug it into a smart plug that has energy monitoring and keep an eye on how often it cycles... Maybe put it downstairs and let the heat convect up." The house does have a downstairs/basement where the furnace is located.

This is not a huge amount of money, but I'd like to figure out a way to heat the house during cold snaps that might be more efficient than the EM heat on the heat pump. Would a radiant oil heater indeed heat the house better and more efficiently than the heat pump? Wouldn't EM heat basically be as efficient as any electric space heater, electric radiant oil heater, etc? The downstairs has an electric hot water heater; I wonder if leaving that on for winter months might be a solution. Right now I turn off the hot water when the house is vacant.

TLDR: would an electric radiant oil heater be more efficient at keeping an empty house at 49F during the winter than a heat pump?