You said something about gas logs so i am assuming you are concerned about a blower /circulatory motor. The fan in this case must be powered up by a Fan Klixon. A fan klixon looks just like a limit switch (usually mounts right beside the limit over the plenum) but works the opposite, when it heats up to around 90f or 100f it kicks on the fan. The contacts in yours are probably fried together. Find the klixon with an F stamped into it. If it has continuity while at room temp it is bad. You can test these fan klixons by heating gently the base of them with a torch. It takes about 30 seconds for the bi-metal inside to pop. heating it makes it have continuity. Next wait to see if it cools down and clicks. Most of the time after a minute it kicks back off. If yours don't then that would explain why the fan runs constantly.