diff --git a/.github/workflows/ci_cron_weekly.yml b/.github/workflows/ci_cron_weekly.yml
index 15d07036d..7bf182c4d 100644
--- a/.github/workflows/ci_cron_weekly.yml
+++ b/.github/workflows/ci_cron_weekly.yml
@@ -27,33 +27,25 @@ jobs:
 
           # We do not use remote data here, since
           # that gives too many false positives due to URL timeouts.
-          - name: Python 3.11 with pre-release version of key dependencies
+          - name: Python 3.12 with pre-release version of key dependencies
             os: ubuntu-latest
-            python: '3.11'
-            toxenv: py311-test-predeps
+            python: '3.12'
+            toxenv: py312-test-predeps
 
           - name: Documentation link check
             os: ubuntu-latest
-            python: '3.10'
+            python: '3.12'
             toxenv: linkcheck
 
     steps:
     - name: Checkout code
-      uses: actions/checkout@v3
+      uses: actions/checkout@v4
       with:
         fetch-depth: 0
     - name: Set up Python
       uses: actions/setup-python@v4
       with:
         python-version: ${{ matrix.python }}
-    - name: Install language-pack-de and tzdata
-      if: ${{ matrix.os == 'ubuntu-latest' }}
-      run: |
-        sudo apt-get update
-        sudo apt-get install language-pack-de tzdata
-    - name: Install graphviz
-      if: ${{ matrix.toxenv == 'linkcheck' }}
-      run: sudo apt-get install graphviz
     - name: Install Python dependencies
       run: python -m pip install --upgrade tox
     - name: Run tests