I know what you mean about leaving something on when you're out, but we have left our little oil filled radiator on when we're out. But only because it's a reliable brand and well made and left on very low - it's finding a balance between no risk and something you feel confident about maybe.
We have one of these - they're supposed to be a reliable brand and we've never had any problems with it. They're not that cheap though, but it has been a godsend - especially when the central heating packed up - they're safe and reliable and have a thermostat.
https://www.amazon.co.uk/Delonghi-TR...illed+radiator
It's a lot cheaper than a space heater or a fan heater to run, especially if left on low. We have one about 2 feet from the cage at night but only on low. It keeps the room at an even temperature if left on low to medium away from the cage as well.
https://www.amazon.co.uk/Delonghi-TR...illed+radiator
I think it's safe to leave on while you're out, as long as you're electrics are up to date. Part of where we live has quite old electrics so we have one of these on the plug socket and run an extension cable from that.
https://www.amazon.co.uk/Masterplug-...extension+lead
I think at this time of year you can't have no heat at all. You could maybe set it on a timer so it came on for a couple of hours mid morning and a couple of hours mid afternoon, but I think they're fine to leave on. We currently don't have central heating and leave one on low 24 hours a day
If you look at the description it has an electrical safety thing built in as well.