A flue stat is a wonderful bit of kit and it can do the world of good for your solid fuel heating system. A flue stat has a probe which is mounted on or near the flue pipe of your stove. When the stove is lit the flue pipe gets hot very fast, the probe also heats up, and when it has reached the set temperature (say 50ºC) then a live is sent to the load unit or pump to turn it on. The major advantage of a pipe stat is that when the stove goes out the pump also shuts down soon after. Using a pipe stat one has to wait until the water in the system has cooled to whatever temperature the pipe stat is set to which can take some time. This can also lead to the your hot water tank loosing heat as the cooling water is pumped around the system. The other problem is that if you have a boiler stove and a conventional boiler then if you do not use a flue stat then you can end up with the situation whereby the stove boiler acts much like a radiator even when the stove itself is out because the conventional boiler is heating he water in the system, which keeps the pipe stat hot, which keeps the pump to the stove on, which circulates the hot water round the stove. Not the end of the world but not ideal either.
If you use a pipe stat then what can also happen is that the pipe gets hot, the pump comes on, floods the boiler with cold water, the pipe gets cold, the pump goes off. This is then repeated for a while which really isn't good for the boiler at all. Using the pipe stat the pump stays on as long as the flue pipe is hot so you don't get this problem. Incidentally you also get around this problem when you use a load unit