Can I get 240 volts to a hard-wired baseboard heater by plugging into a nearby outlet?
You can run a 240V heater on 120V if you really want to, but it'll be weak tea, operating at 1/4 of power.  

You could attempt what you hope, but it will require completely redoing the circuit wiring, to have 2 hots and a neutral in the same cable, at least up to the point where a 120V-only subcircuit branches off. All the conductors must be in the same cable. You cannot grab one hot from this cable and another hot from another cable.  

Also, the fixed loads on each half of the circuit must account for less than 50% of circuit capacity.  Otherwise you can't have any receptacles on it at all.  This is per pole, so if you have a 6 amp heater on both poles obviously, and a 5A sump pump on one pole, that pole can't have any receptacles.  

You must use a 2-pole breaker with 240V between the poles, otherwise you create a serious overload hazard (and also the heater won't work). An example of a bad breaker to use is a double-stuff that fits in one space.  

Doing this type of wiring correctly is hard, and easy to get wrong.  It's harder than using punctuation, for instance.