In my experience, space heaters, electric cars, and even an electric tea kettle have all at one time or another served as excellent “bad wiring detectors.” Read: I’ve melted a few outlets. Fortunately, the materials used to make them are flame retardant so it hasn’t done more damage than give me a good scare.
I now always and obsessively check the temperature on the plug. More than slightly warm is an indicator of a developing problem, and the heat is self reinforcing as the contacts expand and the connection degrades. Often the issue is hidden: it’s loose screws on the back side of the outlet, rather than the plug itself. Poorly mounted outlets that move as you plug into them are especially prone to working loose. Before I was comfortable sleeping with the heater on I would probably check the breakers and inlet plug too. But I’m admittedly paranoid.
If the wiring is in good shape then 1500W is totally fine, but it is at the upper limit of what a regular outlet can handle. A 750W setting, meanwhile, will generate 1/4 the heat in any wiring (P = I ^ 2 x R, I is halved) and would therefore worry me much less.