Would this work as a batch file? (replace filename.txt with the file you want to delete and add lines as necessary). Test it first, i dunno if this would work, but it should I would think. I think that NET VIEW will show all computers on the network.
Code:
@echo off
net view > systemsonnetwork.txt
:{BEGIN}add more lines like below for each file or filespec you want to delete if it wont fit on 1 line
for /f " tokens=1 " %%s in (systemsonnetwork.txt) do dir "%%s\c$\filename.txt *.tmp ~*.*" /s/a/b >> filestodelete.txt
:{END}add more lines like below for each file or filespec you want to delete if it wont fit on 1 line
for /f " tokens=1 " %%t in (filestodelete.txt) do del "%%t" >> deletelog.txt
edit: missed a quote