FWIW, I fixed this problem by changing the Windows TMP environment variable from my C drive, which was low on space, to a large external (USB 3.0) hard drive with plenty of space. ArcHydro then had sufficient space for the temp files and this fixed the error. The second solution here helped me in deciding this course of action.
Note that I tried changing the location of temp files in Arc Advanced Settings Utility but this had no effect (the temp files were still being written to the C drive).
Changing the TMP environment variable and restarting the machine was the only way I could get Arc Hydro (AH) to redirect the temp files. Note that you can check/confirm where AH is writing the temp files in the AH toolbar: ApUtilties > Additional Utilities > Clean User's Temp Folder.
Hope this helps,
Garret