diff --git a/doc/plotting.rst b/doc/plotting.rst
index ea9816780a7..f3d9c0213de 100644
--- a/doc/plotting.rst
+++ b/doc/plotting.rst
@@ -657,7 +657,7 @@ Additionally, the boolean kwarg ``add_guide`` can be used to prevent the display
 
 .. ipython:: python
 
-    ds.w.values = [1, 2, 3, 5]
+    ds = ds.assign(w=[1, 2, 3, 5])
     @savefig ds_discrete_legend_hue_scatter.png
     ds.plot.scatter(x='A', y='B', hue='w', hue_style='discrete')
 
diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 86272cf8710..40307827bc9 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -22,6 +22,12 @@ v0.15.1 (unreleased)
 Breaking changes
 ~~~~~~~~~~~~~~~~
 
+- Raise an error when assigning to the ``.values`` or ``.data`` attribute of
+  dimension coordinates i.e. ``IndexVariable`` objects. This has been broken since
+  v0.12.0. Please use :py:meth:`DataArray.assign_coords` or :py:meth:`Dataset.assign_coords`
+  instead. (:issue:`3470`, :pull:`3862`)
+  By `Deepak Cherian <https://github.com/dcherian>`_
+
 New Features
 ~~~~~~~~~~~~
 
diff --git a/xarray/core/variable.py b/xarray/core/variable.py
index 1ec6512e4fb..c9addeefb04 100644
--- a/xarray/core/variable.py
+++ b/xarray/core/variable.py
@@ -2104,9 +2104,17 @@ def load(self):
     # https://github.com/python/mypy/issues/1465
     @Variable.data.setter  # type: ignore
     def data(self, data):
-        Variable.data.fset(self, data)
-        if not isinstance(self._data, PandasIndexAdapter):
-            self._data = PandasIndexAdapter(self._data)
+        raise ValueError(
+            f"Cannot assign to the .data attribute of dimension coordinate a.k.a IndexVariable {self.name!r}. "
+            f"Please use DataArray.assign_coords, Dataset.assign_coords or Dataset.assign as appropriate."
+        )
+
+    @Variable.values.setter  # type: ignore
+    def values(self, values):
+        raise ValueError(
+            f"Cannot assign to the .values attribute of dimension coordinate a.k.a IndexVariable {self.name!r}. "
+            f"Please use DataArray.assign_coords, Dataset.assign_coords or Dataset.assign as appropriate."
+        )
 
     def chunk(self, chunks=None, name=None, lock=False):
         # Dummy - do not chunk. This method is invoked e.g. by Dataset.chunk()
diff --git a/xarray/tests/test_accessor_dt.py b/xarray/tests/test_accessor_dt.py
index 20a9283e32c..b3640722106 100644
--- a/xarray/tests/test_accessor_dt.py
+++ b/xarray/tests/test_accessor_dt.py
@@ -80,7 +80,7 @@ def test_strftime(self):
     def test_not_datetime_type(self):
         nontime_data = self.data.copy()
         int_data = np.arange(len(self.data.time)).astype("int8")
-        nontime_data["time"].values = int_data
+        nontime_data = nontime_data.assign_coords(time=int_data)
         with raises_regex(TypeError, "dt"):
             nontime_data.time.dt
 
@@ -213,7 +213,7 @@ def setup(self):
     def test_not_datetime_type(self):
         nontime_data = self.data.copy()
         int_data = np.arange(len(self.data.time)).astype("int8")
-        nontime_data["time"].values = int_data
+        nontime_data = nontime_data.assign_coords(time=int_data)
         with raises_regex(TypeError, "dt"):
             nontime_data.time.dt
 
diff --git a/xarray/tests/test_dask.py b/xarray/tests/test_dask.py
index 923b35e5946..538dbbfb58b 100644
--- a/xarray/tests/test_dask.py
+++ b/xarray/tests/test_dask.py
@@ -1276,7 +1276,7 @@ def test_token_changes_when_data_changes(obj):
     assert t3 != t2
 
     # Change IndexVariable
-    obj.coords["x"] *= 2
+    obj = obj.assign_coords(x=obj.x * 2)
     with raise_if_dask_computes():
         t4 = dask.base.tokenize(obj)
     assert t4 != t3
diff --git a/xarray/tests/test_variable.py b/xarray/tests/test_variable.py
index 525a005c601..116466e112d 100644
--- a/xarray/tests/test_variable.py
+++ b/xarray/tests/test_variable.py
@@ -538,8 +538,7 @@ def test_copy_index_with_data(self):
         orig = IndexVariable("x", np.arange(5))
         new_data = np.arange(5, 10)
         actual = orig.copy(data=new_data)
-        expected = orig.copy()
-        expected.data = new_data
+        expected = IndexVariable("x", np.arange(5, 10))
         assert_identical(expected, actual)
 
     def test_copy_index_with_data_errors(self):
@@ -547,6 +546,10 @@ def test_copy_index_with_data_errors(self):
         new_data = np.arange(5, 20)
         with raises_regex(ValueError, "must match shape of object"):
             orig.copy(data=new_data)
+        with raises_regex(ValueError, "Cannot assign to the .data"):
+            orig.data = new_data
+        with raises_regex(ValueError, "Cannot assign to the .values"):
+            orig.values = new_data
 
     def test_replace(self):
         var = Variable(("x", "y"), [[1.5, 2.0], [3.1, 4.3]], {"foo": "bar"})