Then I heard the dripping.
The radiator had started leaking water around the valve. I closed the valve all the way, really hard. Leaking continued. I opened the valve all the way. Leaking continued. Closed. Leaking. I stepped back a few feet, thinking what to do about it, and I noticed my sock feeling wet. That's funny, I'd been really careful not to step in the wet spot near the radiator.
The water had soaked below the floorboards and was coming up through the cracks.
Many, many hours later, after calling about six different plumbers, two of whom even answered, one at least claimed someone was coming at 9am, and who showed up at 11am, only to charge me $85 for saying that the whole valve needed to be replaced at a cost of $380, but who then quoted, in a mumble on his cellphone, the price of replacing the valve to his manager at $350 --- sketchy, that, so I insisted that I had to ask my landlord before embarking on any significant repairs. My landlord said his fix-it guy would come at noon.
And so I waited. And changed out the tupperware container holding the dripping water every half an hour. And waited. And called my landlord repeatedly during the day, who didn't answer. And waited. And called two more plumbers, who didn't answer. And waited. Until finally K came over and brillantly suggested the obvious-in-hindsight remedy of going down the street to the home goods store and at least getting a bigger fucking basin to hold the water in.
Which we got home and jury-rigged a dustpan to funnel the water into it, because the internet taught me that.
My landlord finally showed up at about 9pm, only to repeat the things I'd tried (open and close valve) and then tried and failed to contain the leak with duct tape. He said he'd have to turn off the heat and try and call his fix-it guy again in the morning.
Had a cold night, got up at 2:30 to find the 12L basin full to the brim and just starting to overflow, and emptied it outside.