I have an adjustable speed fan on my fireplace and I would like to have a timer so the fan will go off. What kind of timer should I use? Most that I have found will not adjust the speed.

Do you want the fan to go off at a specific time? You could just use a basic timer. Do you want the fan to go off when the outlet air temperature is below a certain point? That would require a line voltage AC thermostat. They are a bit harder to come by, but they exist. They look like an electric strip heat thermostat. Are you suggesting that you want a timer that will adjust the speed? Now THAT will be a trick, but I can envision the equipment and circuit. It won't be cheap and the more capability, the more $$.

Describe your requirements a bit more fully. I can't read your mind.

I am picturing a heat recirculating prefab fireplace, am I getting close? If so you have a roatry or stepped speed control on the wall near the fireplace. You can interrupt the power to that control with a simple mechanical clocklike wind timer frequently used in bathrooms. Twist the knob and it will run for an hour or less. Do you need more time than that?