My roommate and I have noticed that, since our apartment faces south and we live right by the Hudson, our apartment is starting to be quite chilly in the evenings, and oftentimes is cooler inside than out. We haven't started turning on our heaters yet, and yesterday she suggested we buy space heaters as a solution for keeping our (fairly empty) apartment warm enough to read or surf the internet in without having to bundle up indoors or have our window heating units running for extended periods of time. (This gets expensive, and we were able to cut our electric bill by 75% by running the AC for short periods in the evenings alone last month.) Naturally, we would unplug and put away said units before we left for work each morning.
Our current built-in units are Islandaire brand under-window units, EZ Series, 42. We haven't picked a space heater yet, but chances are I'd just pick one up from Target.
Best Answer
Looking at the unit you linked to (and your comment on waiting for the "cycle" to finish), it appears to be a heat pump. Heat pumps are typically more efficient than electric radiators (e.g. a plug in space heater). They lose efficiency as the outside temperature falls, and eventually you should switch over to emergency or electric heat, which should be built-in to this unit. This is identical to the heat source you would have with a space heater. I doubt you'll see more efficiency out of a space heater (it all depends on the individual units), but if you do, it wouldn't be until it's very cold out.
Side note: The point to switch to electric heating is somewhere around the freezing temperature. I've seen comments ranging from 40F to 20F, that that may also vary from one unit to another. Depending on the unit, this switch may be automatic, or you may have to manually enabled it. If you get down to freezing outside and can't get above 65F inside, then I'd manually flip to electric heat.