diff --git a/gwcs/coordinate_frames.py b/gwcs/coordinate_frames.py
index 5131a4d4..ead793ba 100644
--- a/gwcs/coordinate_frames.py
+++ b/gwcs/coordinate_frames.py
@@ -552,6 +552,13 @@ def _convert_to_time(self, dt, *, unit, **kwargs):
         if not hasattr(dt, 'unit'):
             dt = dt * unit
 
+        is_nan = np.isnan(dt)
+        if is_nan.any():
+            dt[is_nan] = 0
+            out = self.reference_frame + dt
+            out[is_nan] = np.nan
+            return out
+
         return self.reference_frame + dt
 
     def coordinate_to_quantity(self, *coords):
diff --git a/gwcs/tests/test_coordinate_systems.py b/gwcs/tests/test_coordinate_systems.py
index 967657f8..6b0149e3 100644
--- a/gwcs/tests/test_coordinate_systems.py
+++ b/gwcs/tests/test_coordinate_systems.py
@@ -203,6 +203,13 @@ def test_temporal_absolute():
     assert t.coordinates("2018-01-01T00:00:00") == Time("2018-01-01T00:00:00", scale='tai')
 
 
+def test_temporal_nan():
+    t = cf.TemporalFrame(reference_frame=Time("2018-01-01T00:00:00"), unit=u.s)
+
+    ret = t._convert_to_time([0, np.nan]*u.s, unit=u.s)
+    assert np.allclose(ret.mask, [False, True])
+
+
 @pytest.mark.parametrize('inp', [
     (10 * u.deg, 20 * u.deg),
     ((10 * u.deg, 20 * u.deg),),