Many, if not most of the little heaters like Ace hardware sells, have a built in thermostat. It is just that they don't work that good. Since they are in the heater they get hot fast with the heater and not the room temperature . Then cool down. they like to cycle on and off It is possible to out guess them and get them set so that they do a workable job. I went ahead and bought a separate one. A 110 volt house/furnace thermostat will work if you understand how to wire it. Yes, a good one cost all most as much as the heater.

This is a link to the a/c heater in case anyone has any thoughts or experience with this type of contraption. It's the edge star ap410hs. I dont understand why it's considered portable because it vents either out the wall or the ceiling. Thanks! Here is a link that might be useful: Portable a/c ,heater

Several manufacturers make large window unit heat pumps with electric backup heat. You sould be able to order one online. As for operating costs, that all depends on your electric rates, and how much you will be using that room.

Tangogirl, I too live in a sunny NYC apt. I cannot (and don't want to) install window A/C's. Years ago I bought a DeLonghi Pinguino PAC that I use only on the 3-4 days per year that the humidity is unbearable. It can handle only one small room, but it does the job, even after all these years. It is fine in a 13X13 room, less effective in a larger one, but there are more powerful models available for larger spaces. The downside of my model is that it requires filling a huge, clumsy tank with water and, at the end of the season, there is some messy maintenance. I'm sure the technology has improved tremendously. When my Pinguino finally dies, I hope to replace it with a much improved new model, but, like you, I have been unable to find much in the way of reviews. I hope your question generates some helpful responses. All my rooms face south and get lots of sun and a delightful river breeze. I find that by managing the windows carefully (open at night, mostly closed by day, with blinds shut) it's quite comfortable -- cooler than outside. What I would really love is old-fashioned awnings. I've just begun looking into this as a possibility, but I anticipate problems from my building. I think it's unfortunate that A/C has come to be considered indispensible. To give up a window and live with the sound of an A/C doesn't seem worth it for a few bad days. It IS summer, after all! PS - I wonder if we know each other. From your handle, I'm guessing you are a fellow tanguera ....If so, you know the best escape of all on a sultry Sunday night is tango at the South Street Seaport.