How can I read a list of filenames from a file in bash?

I'm trying to write a bash script that will process a list of files whose names are stored one per line in an input file, something the likes of

find . -type f -mtime +15 > /tmp/filelist.txt
for F in $(cat /tmp/filelist.txt) ; do
  ...
done;

My problem is that filenames in filelist.txt may contain spaces, so the snipped above will expand the line

my text file.txt

to three different filenames, my, text and file.txt. How can I fix that?