engine: show temperature and wall heat in fluid results

Route saved temperature through slices, obstacle surfaces, streamlines and both result views, with availability and model units shared by commands and the UI. Show signed obstacle heat histories per complete face area at the selected frame, leaving unrecorded times uncoloured and retaining the saved slice settings.

Part of #157.

docs/control-protocol.md

@@ -139,3 +139,28 @@ factorization's supernodes, the tet mesher's refinement and improvement passes,
 attempts) and stops with `cancelled`, leaving the model unchanged. One job runs at a
 time; another long command meanwhile is refused, naming the job. The MCP server's `solve` and
 `mesh` tools wait for the reply.
+
+## Heated flow results
+
+A solved fluid step with temperature in every saved frame offers `temperature` in the
+Results field list and through `results.contour`, `results.slice`, `results.surface` and
+`results.streamlines` (`{"field":"temperature"}`). Slices and obstacle surfaces sample
+fluid-cell temperature; streamline colours sample temperature along the velocity traces.
+The legend and existing `solve.probe` use the model's temperature scale, without conversion.
+An isothermal step hides the field and rejects an explicit request with an explanation.
+The frame slider and `results.frame` select the field's time, including the initial frame.
+
+`results.surface {"field":"wall_heat_flux","frame":10}` shows the signed heat received
+by each obstacle face divided by that face's complete tessellated geometric area. Positive
+values heat the wall; a hot wall heating the fluid is negative. This is a face average,
+not a resolved local distribution. The legend uses the model's consistent power/area unit:
+for mm–tonne–second it is mW/mm² (not W/mm²); other systems follow their own units.
+
+Wall heat uses the recorded face-group histories, linearly interpolated at the shown frame
+only between recorded times. The initial frame precedes the history and remains uncoloured;
+no heat is invented or extrapolated. Recorded adiabatic faces are zero. Unrecorded/imported
+faces remain in their own colour. The command reply includes `wall_heat.faces` with body,
+face, area, power and flux (null when unavailable), plus the sign and sampling convention.
+This surface-only field suppresses the slice and leaves streamlines plain; selecting a cell
+field restores the saved slice settings. `results.contour` also selects the wall field and
+controls its bands/range. The desktop and headless picture use the same mapping and palette.

docs/features.md

@@ -160,7 +160,7 @@ the control channel and AI agents over MCP (docs/mcp.md) run the same commands.
 | Plots | Path Plot — Plot a quantity along a path | coming soon (M9) |  |
 | Plots | Cut — Section cuts through the model | coming soon (M9) |  |
 | Plots | Display Group — Show and hide parts of the model | coming soon (M9) |  |
-| Plots | Streamlines — A fluid step's streamlines coloured by speed, its velocity or pressure on a slice, and the obstacles coloured by the flow | ready | `results.streamlines`, `results.slice`, `results.surface` |
+| Plots | Streamlines — A fluid step's velocity, pressure or temperature on slices and obstacles, speed or temperature along streamlines, and signed wall heat per area | ready | `results.streamlines`, `results.slice`, `results.surface` |
 | Files | Export VTU — Write a solved step as VTK unstructured grids for ParaView | ready | `results.export.vtu` |
 | Files | Read Results — Read results in public formats | coming soon (M9) |  |
 | Files | Convergence — Mesh convergence studies | coming soon (M9) |  |