diff --git a/src/_pytest/assertion/rewrite.py b/src/_pytest/assertion/rewrite.py
index ded658ba2..96ac0d9bf 100644
--- a/src/_pytest/assertion/rewrite.py
+++ b/src/_pytest/assertion/rewrite.py
@@ -52,7 +52,6 @@ else:
 
 assertstate_key = StashKey["AssertionState"]()
 
-
 # pytest caches rewritten pycs in pycache dirs
 PYTEST_TAG = f"{sys.implementation.cache_tag}-pytest-{version}"
 PYC_EXT = ".py" + (__debug__ and "c" or "o")
@@ -945,7 +944,8 @@ class AssertionRewriter(ast.NodeVisitor):
 
     def visit_NamedExpr(self, name: namedExpr) -> Tuple[namedExpr, str]:
         # This method handles the 'walrus operator' repr of the target
-        # name if it's a local variable or _should_repr_global_name() thinks it's acceptable.
+        # name if it's a local variable or _should_repr_global_name()
+        # thinks it's acceptable.
         locs = ast.Call(self.builtin("locals"), [], [])
         target_id = name.target.id  # type: ignore[attr-defined]
         inlocs = ast.Compare(ast.Str(target_id), [ast.In()], [locs])
@@ -981,8 +981,11 @@ class AssertionRewriter(ast.NodeVisitor):
                 # cond is set in a prior loop iteration below
                 self.expl_stmts.append(ast.If(cond, fail_inner, []))  # noqa
                 self.expl_stmts = fail_inner
-                if isinstance(v, ast.Compare):
-                    if isinstance(v.left, namedExpr) and (
+                # Check if the left operand is a namedExpr and the value has already been visited
+                if (
+                    isinstance(v, ast.Compare)
+                    and isinstance(v.left, namedExpr)
+                    and (
                         v.left.target.id
                         in [
                             ast_expr.id
@@ -990,16 +993,11 @@ class AssertionRewriter(ast.NodeVisitor):
                             if hasattr(ast_expr, "id")
                         ]
                         or v.left.target.id == pytest_temp
-                    ):
-                        pytest_temp = f"pytest_{v.left.target.id}_temp"
-                        self.variables_overwrite[v.left.target.id] = pytest_temp
-                        v.left.target.id = pytest_temp
-
-                    elif isinstance(v.left, ast.Name) and (
-                        pytest_temp is not None
-                        and v.left.id == pytest_temp.lstrip("pytest_").rstrip("_temp")
-                    ):
-                        v.left.id = pytest_temp
+                    )
+                ):
+                    pytest_temp = util.compose_temp_variable(v.left.target.id)
+                    self.variables_overwrite[v.left.target.id] = pytest_temp
+                    v.left.target.id = pytest_temp
             self.push_format_context()
             res, expl = self.visit(v)
             body.append(ast.Assign([ast.Name(res_var, ast.Store())], res))
@@ -1075,6 +1073,7 @@ class AssertionRewriter(ast.NodeVisitor):
 
     def visit_Compare(self, comp: ast.Compare) -> Tuple[ast.expr, str]:
         self.push_format_context()
+        # We first check if we have overwritten a variable in the previous assert
         if isinstance(comp.left, ast.Name) and comp.left.id in self.variables_overwrite:
             comp.left.id = self.variables_overwrite[comp.left.id]
         left_res, left_expl = self.visit(comp.left)
@@ -1093,7 +1092,7 @@ class AssertionRewriter(ast.NodeVisitor):
                 and isinstance(left_res, ast.Name)
                 and next_operand.target.id == left_res.id
             ):
-                next_operand.target.id = f"pytest_{left_res.id}_temp"
+                next_operand.target.id = util.compose_temp_variable(left_res.id)
                 self.variables_overwrite[left_res.id] = next_operand.target.id
             next_res, next_expl = self.visit(next_operand)
             if isinstance(next_operand, (ast.Compare, ast.BoolOp)):
diff --git a/src/_pytest/assertion/util.py b/src/_pytest/assertion/util.py
index fc5dfdbd5..e5bf201c7 100644
--- a/src/_pytest/assertion/util.py
+++ b/src/_pytest/assertion/util.py
@@ -520,3 +520,7 @@ def running_on_ci() -> bool:
     """Check if we're currently running on a CI system."""
     env_vars = ["CI", "BUILD_NUMBER"]
     return any(var in os.environ for var in env_vars)
+
+
+def compose_temp_variable(original_variable: str) -> str:
+    return f"pytest_{original_variable}_temp"