This assembly circulates room air through a vent in the fireplace, around the firebox wall and forces heated air back into the room.
This assembly is straight wired to a switch. I have removed the assembly but I cannot locate any identifying info due to it being burned in house fire. I want to locate a source to purchase a replacement.

You can call a heating contractor. If you plan on doing it yourself then you would have to dissassemble or remove the motor and assembly and take it to an electric motor supply place so that they can match it . There are probale some specs ingraved on the body of the motor.

I currently have a 36,000 BTU ventless gas log unit in my fireplace and am contemplating exchanging it for a woodburning heat exhanger. The reason is that the ventless gas insert heats the room it's in but not the rest of the house. I have been told that I can't use a fan with the ventless logs because it can produce dangerous carbon monoxide. Since I don't want to spend a lot of money by getting a chimney reline and woodburning insert (I have an unlimited supply of free wood) I was presented with a woodburning heat exchanger, which comes with a blower to distribute heat throughout the house. I was wondering if anyone has any experience with these and if the benefits will be great enough to justify the cost (around $1500) of replacing the ventless gas logs I currently have. The ventless gas logs obviously use gas, which costs money, so I'm looking for a good alternative for heating the house with free wood, minimizing my furnace use while wanting a payback on my investment in less than 5 years, which a regular woodburning insert would cause.

We have a HUGE wood burning fireplace and we love it. We only use it for a few hours in the winter evenings though, mainly because we love the look, sound and mood in provides. The rest of the day we run a gas Munchkin to heat the house.

Hauling in the logs is a lot of work, cleaning out the ash is also a hassle.
You cannot possibly stack the fireplace to last through the night, you would have to get up during the night quite a few times to keep the fire going.
Once the fire is out, your house would get cold fairly quickly - well, depending on how cold your winters are. Ours is as low as -20F.
If you leave for work in the morning, you will likely to come home to a very cold home, your pipes might freeze etc...
If you are home all the time, you would want the fire to burn continuously (putting logs on it every 2-3 hours or so), leaving you no chance to clean out the ash. It takes over 12 hours for the ash to cool off enough to handle it safely.

Good idea for you to convert? It really depends on your tolerance and on how much you are willing to work in order to save on gas. In my home, I cannot see it working out without the gas furnace.
Best of luck!