diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 5c2d099ed3119..febfa59b7e962 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -370,6 +370,7 @@ MultiIndex
 ^^^^^^^^^^
 
 - Bug in :meth:`DataFrame.xs` when used with :class:`IndexSlice` raises ``TypeError`` with message ``"Expected label or tuple of labels"`` (:issue:`35301`)
+- Bug in :meth:`DataFrame.reset_index` with ``NaT`` values in index raises ``ValueError`` with message ``"cannot convert float NaN to integer"`` (:issue:`36541`)
 -
 
 I/O
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 3aa1317f6db6d..48391ab7d9373 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -73,7 +73,7 @@
     ABCSeries,
 )
 from pandas.core.dtypes.inference import is_list_like
-from pandas.core.dtypes.missing import isna, notna
+from pandas.core.dtypes.missing import is_valid_nat_for_dtype, isna, notna
 
 if TYPE_CHECKING:
     from pandas import Series
@@ -1559,6 +1559,11 @@ def construct_1d_arraylike_from_scalar(
             dtype = np.dtype("object")
             if not isna(value):
                 value = ensure_str(value)
+        elif dtype.kind in ["M", "m"] and is_valid_nat_for_dtype(value, dtype):
+            # GH36541: can't fill array directly with pd.NaT
+            # > np.empty(10, dtype="datetime64[64]").fill(pd.NaT)
+            # ValueError: cannot convert float NaN to integer
+            value = np.datetime64("NaT")
 
         subarr = np.empty(length, dtype=dtype)
         subarr.fill(value)
diff --git a/pandas/tests/series/indexing/test_multiindex.py b/pandas/tests/series/indexing/test_multiindex.py
index e98a32d62b767..0420d76b5e8a8 100644
--- a/pandas/tests/series/indexing/test_multiindex.py
+++ b/pandas/tests/series/indexing/test_multiindex.py
@@ -1,8 +1,10 @@
 """ test get/set & misc """
 
+import pytest
 
 import pandas as pd
 from pandas import MultiIndex, Series
+import pandas._testing as tm
 
 
 def test_access_none_value_in_multiindex():
@@ -20,3 +22,30 @@ def test_access_none_value_in_multiindex():
     s = Series([1] * len(midx), dtype=object, index=midx)
     result = s.loc[("Level1", "Level2_a")]
     assert result == 1
+
+
+@pytest.mark.parametrize(
+    "ix_data, exp_data",
+    [
+        (
+            [(pd.NaT, 1), (pd.NaT, 2)],
+            {"a": [pd.NaT, pd.NaT], "b": [1, 2], "x": [11, 12]},
+        ),
+        (
+            [(pd.NaT, 1), (pd.Timestamp("2020-01-01"), 2)],
+            {"a": [pd.NaT, pd.Timestamp("2020-01-01")], "b": [1, 2], "x": [11, 12]},
+        ),
+        (
+            [(pd.NaT, 1), (pd.Timedelta(123, "d"), 2)],
+            {"a": [pd.NaT, pd.Timedelta(123, "d")], "b": [1, 2], "x": [11, 12]},
+        ),
+    ],
+)
+def test_nat_multi_index(ix_data, exp_data):
+    # GH36541: that reset_index() does not raise ValueError
+    ix = pd.MultiIndex.from_tuples(ix_data, names=["a", "b"])
+    result = pd.DataFrame({"x": [11, 12]}, index=ix)
+    result = result.reset_index()
+
+    expected = pd.DataFrame(exp_data)
+    tm.assert_frame_equal(result, expected)