There are plenty of solutions for this simple problem.
The safety aspect is a couple of things:
- ensure nothing is draped over the heater before you turn it on. This is the hard one to do with any automation. Maybe with "AI" on cameras this could be done in the future. Of course that would then require a camera in the bedroom...
- ensure you have electrically the right capacity relay switch to handle the amperage of the heater. This one is easy. Many "appliance switches" are available in multiple technologies
- Is this a one shot project? Or to be part of a larger ecosystem of automated devices? This is the hardest to answer. If larger then pick your automation controller first, then your technical means of support of the appliance switch (ie: Z-Wave vs, Zigbee, vs. proprietary Wifi). Once those two choices are made, then your list of Appliance Switches to use is a shorter list.
If this is a One shot project, then there are proprietary smartphone apps that talk Wifi or bluetooth to matching appliance switches. But then your phone needs to be on the same network / proximity of the heater. That then starts to point on some of the benefits of a "real" control system that is always available to trigger automation tasks (ie: scheduled events like turning a heater on at 6AM during work days, and 8AM on weekends). Your phone does not then need to be present.