A burner will run on bio diesel, and the output of heat would be dependant on the type of biodiesel that is being used. B5 will output more then B99 would due to diesel being less in the B99 vs the B5.
I used to run a SVO (Straight veggy oil) setup on 2 cars I had probably close to 10 years ago now. Did 60k miles between them and since I got the oil for free the learning curve was not as expensive.
I thought about this when I got into the pressure washing business as a way to save money, but I came to the conclusion that I needed reliability more then I needed the savings. I would though get commercial Biodiesel if it was sold around here, but with no options I just used the regular stuff. If you have time and extra equipment play around with it and see how it goes. It can be very messy and cause issues, but if you save lots on diesel it can be worth it.
I also live in a cold climate, so you guys down south won't have the same issues I have.