The heating element -- the part that runs the length of the baseboard and is responsible for providing heat -- is generally made of a long piece of metal that’s electrically fed, causing it to warm up. Not only does the metal stripping heat but so do the smaller metal slats that run the length of the element. These direct heat into the room. When the metal heats up, it expands; when it cools, it shortens. This “give-and-take” drastic change in size causes the element to click, especially when it cools down. Normally this goes by unnoticed, but if a room is quiet, it can become bothersome.
If the noise of the heating/cooling becomes too annoying, one way to alleviate the problem is try adjusting the thermostat in the room or home to a temperature that doesn’t allow the heater to cool completely. The upside to this approach is that the element won’t be able to cool down considerably and the heat will turn back on not long after it has been turned off. This heats the element again and reduces the clicking noise. The downside is that this will most certainly increase your monthly home heating cost.
In some cases, older homes feature water-fed baseboard heating similar to radiators and opposed to more modern electrical heating. This style of heating is typically fed directly from the home’s boiler. As the heated water leaves the boiler, it is pumped upward through the piping, and the piping -- rather than the element -- expands. This causes the piping to rub against the hole or holes in the flooring where the piping enters the room. As water is pumped, it bumps the floor and causes the clicking. Simply enlarging the holes where the pipe enters gives the pipe more room to move.
Most but not all modern baseboard heating elements are supported to a series of plastic mounting brackets. The number of brackets in your heater depends on how long the heater is. By removing the front facing on the heater you should be able to see the brackets under the element. If there are no brackets, chances are the expanding element is rubbing the base of the heater since it isn’t supported. Purchasing these plastic supports aftermarket at a home improvement store and installing them yourself should alleviate the problem.