The window mounted h/p units would work fine. They are designed for a 300 sqft room. I have basically the same thing and it works awesome. I check with several diff. Thermostats to make sure it keeps my room to temp. Keeps it within one degree of set point in the summer and pretty much dead on in the winter. I work in the industry and the controls on these types of units have come leaps and bounds in the past few years. I don't like lagers all that much, so I haven't tested it on low temps in the summer, but it shouldn't be a problem in the winter. I am about to change over to a mini split unit, because my supplier is gonna give me one. These are the ultimate fermenting room unit. Everyone should have one.
Fermenters: beer and cider
Bottled: lots of beer and cider :)
"BEER....The cause of, and solution too, all of life's problems"