diff --git a/src/jinja2/bccache.py b/src/jinja2/bccache.py
index f8bdf3032..e9dca6d61 100644
--- a/src/jinja2/bccache.py
+++ b/src/jinja2/bccache.py
@@ -279,31 +279,28 @@ def dump_bytecode(self, bucket: Bucket) -> None:
         # https://github.com/pallets/jinja/issues/1654.
         fn = self._get_cache_filename(bucket)
 
-        # Name of the temporary file
-        tempfn: t.Optional[str] = None
+        f = tempfile.NamedTemporaryFile(
+            mode="wb",
+            dir=os.path.dirname(fn),
+            prefix=os.path.basename(fn),
+            suffix=".tmp",
+            delete=False,
+        )
 
         def clean() -> None:
-            if tempfn:
-                try:
-                    os.remove(tempfn)
-                except OSError:
-                    # This can occur if another process called
-                    # clear().  Also, on Windows, this might occur for
-                    # reasons beyond our control.  For example,
-                    # another process such as the Windows Search
-                    # indexer or an antivirus product may be holding
-                    # the file open, preventing deletion.
-                    pass
+            try:
+                os.remove(f.name)
+            except OSError:
+                # This can occur if another process called
+                # clear().  Also, on Windows, this might occur for
+                # reasons beyond our control.  For example,
+                # another process such as the Windows Search
+                # indexer or an antivirus product may be holding
+                # the file open, preventing deletion.
+                pass
 
         try:
-            with tempfile.NamedTemporaryFile(
-                mode="wb",
-                dir=os.path.dirname(fn),
-                prefix=os.path.basename(fn),
-                suffix=".tmp",
-                delete=False,
-            ) as f:
-                tempfn = f.name
+            with f:
                 bucket.write_bytecode(f)
         except BaseException:
             clean()
@@ -319,7 +316,7 @@ def clean() -> None:
             #     For example, an antivirus product or search indexer
             #     process.
             #  3) Another process might clear() just before this rename.
-            os.rename(tempfn, fn)
+            os.rename(f.name, fn)
         except OSError:
             clean()
         except BaseException: