While not a text file nor using chron, you can use a combination of git and etckeeper to achieve the same result.
etckeeper allows the contents of /etc to be stored in a Version
Control System (VCS) repository. It integrates with APT and
automatically commits changes to /etc when packages are installed or
upgraded. Placing /etc under version control is considered an industry
best practice, and the goal of etckeeper is to make this process as
painless as possible. - from the Ubuntu Documentation
Start by installing git:
sudo apt-get install git
Configure git for the root account:
sudo git config –global user.name “Your Name”
sudo git config –global user.email youremailaddress
Then install etckeeper:
sudo apt-get install etckeeper
Because git is already installed this will not only install etckeeper, but initialize the database and make an initial commit of the files in /etc.
You can check the status of the repository with the following commands:
sudo git status
you should see the following:
On branch master
nothing to commit, working directory clean
Now anytime you run an apt command (install, purge etc.) Etckeeper will automatically add a commit to the underlying git repo, noting the changes and time they were made.
You can view all packages installed, updated and removed using the git log command.
sudo git log
As I mentioned this is not a text file, but the git log can certainly be turned into a text file if needed. This also has the advantage of being automatic and tracking any changes made manually to your systems config files.
I wrote a blog post with additional details and some config settings you may want to make available here.