I have been wondering if this is possible or not? If you wanted to run a 240v ac baseboard heater on 120v ac couldn't you just just use a 120v ac to 240v ac step-up tranformer? I already know what happens if you would run a 240v baseboard on a 120v circuit, the baseboard heater would draw 1/4 the power.
Heaters are cheap. There'd be no reason to do this!
An electric heater is one of the simplest appliances in the world -- so it is inherently very low-cost. It's not cheaply made, it's just simple enough it doesn't cost very much to make one.
It will be cheaper to buy the right heater than adapt the wrong heater.
I imagine you got this thing gifted to you, and you have no idea how much heaters actually cost. Go find out; the typical baseboard heater is a Cadet, and they are around $50 for a big one. You can't buy a step-up transformer for that, you are in peril of spending $150 to change the voltage on a $50 heater. Don't do that lol.
Now if you're stuck with the common receptacle circuit in your house, Those circuits are not magic. They cannot carry unlimited amounts of power, in fact USA circuits are particularly limited to a measly 1440W, or just one of those portable heaters. So it wouldn't matter if you got a big baseboard heater that is 120V, you couldn't hook it up anyway.
Contrast with a properly wired 240V circuit, which can carry 3840 watts, or almost 3x as much, that is why baseboard heaters are mostly 240V.
I'll assume you are just trying to avoid running a new wire to the baseboard heater.
You could use a transformer at the panel to step up the voltage from 120 to 240 and run more power at the same current on the same wire.
However you'd have to feed the transformer from a big single pole OCPD and suitably sized wire.
I can't see a situation where it wouldn't be easier to just put in the 240V breaker, even if you were out of space in the panel and had to install a small subpanel.
You could, but it wouldn't be at all cost effective
The problem with stepping up the voltage is that you're stepping down the current in the process, as a transformer can't put any more power out than it gets in. As a result, you would need to run wire into the transformer suited for twice the heater's nameplate current rating, meaning that you would need much more costly wire atop having to pay for a transformer. This is quite uneconomical compared to simply running 240V in just about all circumstances.
ONLY IF your circuit is used only for heaters, AND all your heaters are 240V AND none of those require neutral connection AND the heaters are hardwired you could re-purpose neutral wire as second live replacing the breaker with a double pole one.