diff --git a/packages/domain/src/domain/sap/rdsap/cert_to_inputs.py b/packages/domain/src/domain/sap/rdsap/cert_to_inputs.py
index b9745fd0..c79cccff 100644
--- a/packages/domain/src/domain/sap/rdsap/cert_to_inputs.py
+++ b/packages/domain/src/domain/sap/rdsap/cert_to_inputs.py
@@ -76,6 +76,7 @@ from domain.sap.worksheet.internal_gains import (
 )
 from domain.sap.worksheet.heat_transmission import (
     DwellingExposure,
+    HeatTransmission,
     heat_transmission_from_cert,
 )
 from domain.sap.climate.appendix_u import external_temperature_c
@@ -690,6 +691,28 @@ def _ventilation_counts(vent: Optional[SapVentilation]) -> _VentilationCounts:
     )
 
 
+def heat_transmission_section_from_cert(epc: EpcPropertyData) -> HeatTransmission:
+    """SAP 10.2 §3 cert→inputs cascade for `heat_transmission_from_cert`.
+
+    Wraps the `_window_total_area_and_avg_u` + `_dwelling_exposure`
+    derivations cert_to_inputs makes internally and returns the full
+    `HeatTransmission` (every (26)..(37) line ref breakdown). Exposed
+    so cascade pin tests can assert each §3 line ref against the U985
+    PDF.
+    """
+    window_total_area, window_avg_u = _window_total_area_and_avg_u(epc.sap_windows)
+    exposure = _dwelling_exposure(epc.dwelling_type)
+    return heat_transmission_from_cert(
+        epc,
+        window_total_area_m2=window_total_area,
+        window_avg_u_value=window_avg_u,
+        door_count=epc.door_count,
+        insulated_door_count=epc.insulated_door_count,
+        insulated_door_u_value=epc.insulated_door_u_value,
+        exposure=exposure,
+    )
+
+
 def ventilation_from_cert(epc: EpcPropertyData) -> VentilationResult:
     """SAP 10.2 §2 cert→inputs cascade for `ventilation_from_inputs`.
 
@@ -1050,20 +1073,9 @@ def cert_to_inputs(
     (inspection_date ≥ 2025-07-01) rather than a per-cert price
     override."""
     dim = dimensions_from_cert(epc)
-    window_total_area, window_avg_u = _window_total_area_and_avg_u(epc.sap_windows)
-    exposure = _dwelling_exposure(epc.dwelling_type)
-    ht = heat_transmission_from_cert(
-        epc,
-        window_total_area_m2=window_total_area,
-        window_avg_u_value=window_avg_u,
-        door_count=epc.door_count,
-        insulated_door_count=epc.insulated_door_count,
-        insulated_door_u_value=epc.insulated_door_u_value,
-        exposure=exposure,
-    )
-
-    # SAP §2 ventilation cascade — see `ventilation_from_cert` for the
-    # cert→inputs mapping rules + spec-default conventions.
+    # SAP §3 heat transmission + §2 ventilation cascades — see the
+    # respective `_from_cert` helpers for cert→inputs mapping rules.
+    ht = heat_transmission_section_from_cert(epc)
     ventilation = ventilation_from_cert(epc)
 
     main = _first_main_heating(epc)
diff --git a/packages/domain/src/domain/sap/worksheet/tests/test_section_cascade_pins.py b/packages/domain/src/domain/sap/worksheet/tests/test_section_cascade_pins.py
index 172ff27a..800c48de 100644
--- a/packages/domain/src/domain/sap/worksheet/tests/test_section_cascade_pins.py
+++ b/packages/domain/src/domain/sap/worksheet/tests/test_section_cascade_pins.py
@@ -16,7 +16,11 @@ from typing import Final
 
 import pytest
 
-from domain.sap.rdsap.cert_to_inputs import cert_to_inputs, ventilation_from_cert
+from domain.sap.rdsap.cert_to_inputs import (
+    cert_to_inputs,
+    heat_transmission_section_from_cert,
+    ventilation_from_cert,
+)
 from domain.sap.worksheet.dimensions import dimensions_from_cert
 from domain.sap.worksheet.tests import (
     _elmhurst_worksheet_000474 as _w000474,
@@ -187,3 +191,45 @@ def test_section_2_line_19_sheltered_sides_matches_pdf(fixture_name: str) -> Non
     assert vent.sheltered_sides == expected, (
         f"§2 (19) {fixture_name}: actual={vent.sheltered_sides}, expected={expected}"
     )
+
+
+# ============================================================================
+# §3 Heat losses + heat loss parameter — LINE_31/33/36/37 aggregates
+# ============================================================================
+
+_SECTION_3_PINS: Final[tuple[tuple[str, str], ...]] = (
+    # (fixture_attr, HeatTransmission attr)
+    ("LINE_31_TOTAL_EXTERNAL_AREA_M2",      "total_external_element_area_m2"),
+    ("LINE_33_FABRIC_HEAT_LOSS_W_PER_K",    "fabric_heat_loss_w_per_k"),
+    ("LINE_36_THERMAL_BRIDGING_W_PER_K",    "thermal_bridging_w_per_k"),
+    ("LINE_37_TOTAL_FABRIC_HEAT_LOSS_W_PER_K", "total_w_per_k"),
+)
+
+
+@pytest.mark.parametrize(
+    "fixture_name,fixture_attr,result_attr",
+    [
+        (fix, line, attr)
+        for fix in _FIXTURES
+        for line, attr in _SECTION_3_PINS
+    ],
+    ids=lambda x: x if isinstance(x, str) else None,
+)
+def test_section_3_line_refs_match_pdf(
+    fixture_name: str, fixture_attr: str, result_attr: str
+) -> None:
+    """§3 cascade pins — every (31)/(33)/(36)/(37) aggregate matches the
+    U985 PDF to abs=1e-4. Per-element breakdowns (26)/(27)/(28a)/(29a)/
+    (30)/(32) are not currently lodged in fixture constants — they're
+    asserted indirectly via the aggregates."""
+    # Arrange
+    mod = _FIXTURES[fixture_name]
+    epc = mod.build_epc()  # type: ignore[attr-defined]
+    expected = getattr(mod, fixture_attr)
+
+    # Act
+    ht = heat_transmission_section_from_cert(epc)
+    actual = getattr(ht, result_attr)
+
+    # Assert
+    _pin(actual, expected, f"§3 {fixture_attr} {fixture_name}")