I have no AC in my condo, only hydronic baseboard heat, currently controlled by an old mercury thermostat. I have a new smart thermostat with a c-wire adapter I want to replace it. Trouble is, I’ve switched every darn switch on the panel (as far as having every breaker switch off at the same time), and the thermostat is still getting power/able to control the heaters. I live in a condo with a common boiler, and there are no zones within my unit, so all baseboards are either on or off, in case that’s relevant. Can I move forward and replace this thing without shutting it off first? This is a little outside my DIY realm of experience so any advice is appreciated!
The reason you need to cut off power when replacing a thermostat is to prevent the wires from touching each other in the process of disconnecting and reconnecting all of them. Assuming it is using 24VAC control (you need to measure it to make sure it's not high voltage), you are not in danger of getting shocked, but if the wrong wires touch each other, it could blow a fuse or damage the equipment.
If you can't turn off the power (lets just assume you can't) then just be very careful and don't let the bare wires touch anything. The best way to do this is tape up each wire as it is disconnected and never have more than one wire un-taped at a time. Treat the wires like live voltage that could shock you to make sure you are being careful enough. A small touch of wires or touching the wrong screw could cause damage to the system.
If the thermostat has a separate mounting plate that the wires connect to, it makes it easier (most common these days). If the wires connect directly to the thermostat, you need to make sure the thermostat is completely off until all wires are disconnected and reconnected.