I agree, at that temperature, 3 weeks should have had some results. I have a beer I just tested after 2-3 weeks and it's carbed and my temperature here is 68 from 6:30am-8:30am, 65 from 8:30am-5:30pm, 68 from 5:30pm-12pm, then 65 from 12 to 6:30 again. Ambient heat from the other apartments keeps it around 65. Sometimes I'll turn the heat up to 70 but very seldomly.
I also agree that the fermentation and carbing can take longer at these lower temperatures, but if you're not getting *any* carbonation at all in 4 weeks, somethings wrong and a higher temperature may not help. When you tested it, was it completely flat? Or just not carbed enough? (We're all assuming you used a certain amount of priming sugar and didn't bottle without, of course).
Otherwise, I do like that yogurt idea. I do the same with yogurt. I fill up a large ceramic pot with hot water and stick it in the oven with other containers. I think for beer, I would use a water temperature of about 80 to get a roughly 75-80 degree ambient temperature. Unless you want it higher of course. For yogurt, I just stick the ceramic insert back into the crockpot and heat it for a while then put it back in to keep going, or just remove some water, boil it and pour it back in. I think I aim for the high 90's when I do yogurt.