Try with python39=3.9.16-1

Author: EliahKagan

.github/workflows/cygwin-test.yml

@@ -30,7 +30,7 @@ jobs:
     - name: Install Cygwin
       uses: cygwin/cygwin-install-action@v4
       with:
-        packages: python39 python39-pip python39-virtualenv git
+        packages: python39=3.9.16-1 python39-pip python39-virtualenv git
         add-to-path: false  # No need to change $PATH outside the Cygwin environment.
 
     - name: Arrange for verbose output
@@ -63,14 +63,11 @@ jobs:
     - name: Update PyPA packages
       run: |
         # Get the latest pip, wheel, and prior to Python 3.12, setuptools.
-        mkdir -- "$(pwd)/tmp"
-        export TEMP="$(pwd)/tmp" TMP="$(pwd)/tmp"
-        python -m pip -vvv --no-cache-dir install -U pip $(pip freeze --all | grep -ow ^setuptools) wheel
+        python -m pip -vvv install -U pip $(pip freeze --all | grep -ow ^setuptools) wheel
 
     - name: Install project and test dependencies
       run: |
-        export TEMP="$(pwd)/tmp" TMP="$(pwd)/tmp"
-        pip install -vvv --no-cache-dir ".[test]"
+        pip -vvv install ".[test]"
 
     - name: Show version and platform information
       run: |