Is it a specific ventilation effect or is it heat soak from the bulkhead and alloy panels around the gearbox being drawn by the top-down airflow in the footwell ? Flip the lid up for a short time and see if the vent effect is still happening ?

It is quite common for the heat soak from the engine to warm the cockpit. In the S2 after a long run my left knee is usually pretty roasted from leaning against the gearbox area in order to avoid resting on the clutch.

Options are greater engine bay venting as far as I am aware.

To reduce the warm engine bay air being drawn into the cabin I have put a second layer of insulation around the intake in front of the windscreen. This raises it up higher and seals against the bonnet underside.

Everyone loves a Morgan. Even me, unless it's broken again.