A retrofit damper should be installed at the top of the chimney and requires a clay tile liner. It is operated from the side of the fire box by a cable.

They are sold through fireplace shops, chimney sweeps and Amazon.com.

Here is a link that might be useful: top damper

The chimney sweep recommended that too, but the price he quoted was $500. This, or something like it, seem slike a more economical way of doing the same task. I saw this on Amazon and I see it is theoretically available at Home Depot:
http://www.homedepot.com/webapp/wcs/stores/servlet/ProductDisplay?storeId=10051&productId=100662572&langId=-1&catalogId=10053&ci_src=14110944&ci_sku=100662572&cm_mmc=shopping-_-googlebase-_-D22X-_-100662572

If you put URL's in the box provided and give it a name, people can click on it.

Would you really take that thing out every time you wanted to use the fireplace? I suspect you will use it once and then throw it away because of the mess it makes or you'll try to start a fire and smoke up the house. Then you'll be back where you started.

If the chimney sweep wants to charge you $340 to attach a $160 damper to the top of the flue tile, you're talking to the wrong guy. Order the damper online and offer him or another chimney sweep $100 to install it.

All that is required is climbing up there with the damper unit and a tube of glue and sticking it on top of the clay flue tile and then dropping the cable down the chimney and securing a bracket to the side of the fire box.

Avoid temporary solutions to permanent problems.

Here is a link that might be useful: installation instructions