Work Energy will be less than or equal to the available Heat Energy.
Total Energy is constant. Unconverted Heat = Original Heat - Work.

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Is there a limit to how much motion you can get from a given amount of heat?
Yes, absolutely. The limit is 100%.

Historically

Sadi Carnot, Lord Kelvin both discuss the maximum amount of motion available from a given amount of heat. They conclude air and steam engines produce the maximum amount of work possible from the heat consumed.

They go on to demonstrate the property of reversibility of vapors, expansion cools vapor and produces a given amount of work. Reverse the expansion (compress) and it takes the same amount of work and raises the temperature back to the starting point.

Absolute equality of the energy of heat and motion.

Science Now

The main, and simple, answer is Energy = Work+Heat. (can't say that enough :)

First, lets explore how much heat can "theoretically" be converted. Lets say we expanded about 8 times the original volume, which converts about half the heat. This leaves half the heat. Lets say we added 600° C of heat before expansion. What is the final heat? Not 300° Kelvin, but 450° Kelvin. The Absolute temperature of room temperature is about 300° Kelvin, or about 30° C. So add 600°C results in 900° Kelvin. Convert half, there is 450° Kelvin left. So of the 600° C fuel heat, we have already converted 450/600= 75% of the fuel heat with a 50% conversion.

Now, are we done? Current engines stop there. But in 1824 Carnot explained if you have a temperature difference you can create a motive force. If we put that extra 150°C, (450-300), in another vapor chamber, we can create another pressure difference, convert a fraction, and repeat. A couple doze pistons and we have effectively converted almost all the 600°C fuel heat we started with.

So, there is no theoretical reason we cannot convert all our fuel heat.

But then we reach the limit. We cannot convert the ambient approximately 300° Kelvin of the heat in our engine. We no longer have a Temperature difference.

Does this mean we can't suck heat out of the air? Yes and no. Our heat engines cannot, but wind driven machines do just that. So its not a fundamental limit of the universe that the heat in the air is unusable, but no one has any machine better than a windmill or sail to do that.