I would suggest doing this with something like a batch file using ImgBurn from the command line.
For example, put the following into Notepad, change ‘d:’ to the drive letter of your Blu-ray drive and save it as “Burn_ISO.bat” inside your browser’s download folder.
set /p imagefile=Enter the ISO file name:
echo Waiting for %imagefile% . . .
ping -n 2 localhost >nul
if not exist %imagefile% goto repeat
echo Burning %imagefile% . . .
"%ProgramFiles(x86)%\imgburn\imgburn" /mode write /src "%imagefile%" /dest d: /start /speed max /verify yes
Start your download of the BDR image, insert a blank BD-R and run the batch file. Enter the full filename of the image, press enter and then leave the PC to download. The batch file will keep checking for the presence of that file name. When it appears, it will launch ImgBurn to burn the image file.
Even if there is a utility to burn while downloading in realltime, personally I would not recommend that method. Not many servers (or ISP connections) can sustain a fast enough speed to burn without persistent start/stop write cycles throughout the disc, potentially reducing the write quality. For example, burning at 4x would require a consistent 144+Mbps throughout the download.