Is there a portable heater that will keep a closet sized room at a constant temperatu

[Beardy]

Buy a thermostat for a reptile enclosure from a pet store and then connect any heat source you fancy to it
Very accurate and simple way to control the temperature

[barrysumpter]

Yes. That's the way I went.
Inkbird ITC-306T WiFi Temperature Controller Aquarium Thermostat with Waterproof Probe Heating Smart Cycle Timer, APP Support Remote Monitor Control : Amazon.com.au: Pet Supplies