There are some old fashioned alternatives to heating brooders without electricity, namely kerosene, but that doesn't thrill me. The fumes and the carbon monoxide would worry me.
Then I googled and found "haybox brooders". But you need to use a pot of boiling water inside the box of straw, and I'm not wild about that idea, either.
That got me thinking about how much heat green grass cuttings puts out as it decomposes. A lot! If you have grass coming in, go mow it and build a nice box to fit under your brooder. You would need to experiment and make sure it's vented to allow oxygen to get in to help decomposition and any gasses to escape. I'd drill holes around the sides so the air can go directly into the decomposing mass.
Make sure you measure the temp since it could get way hotter than is safe for baby poultry! This is an untested idea! But I'm willing to bet you could get the right temp by adjusting the height of the brooder as it sits over the compost box.
Also, you would not want to heat your entire brooder. The ducklings will need the majority of the brooder to be cool so they can go from warming themselves over the hot spot to cooling themselves if they get too warm. Also they need cool ambient temps in order to feather out efficiently.