Why engine oil can affect hot running
Engine oil reduces friction, protects moving parts and helps the engine cope with heat. If the oil level is low, the oil is tired, or the grade is wrong for the engine, the engine can become less well protected and more heat can build where it is least welcome.
Low oil level is the first check
Before blaming the radiator, fan, thermostat or water pump, check the oil level with the dipstick. A low oil level can reduce lubrication and make the engine work harder than it should. It is one of those checks that takes seconds and can save a surprising amount of head-scratching.
The correct oil type and grade matter
The factory recommendation was a mineral-based engine oil with a grade of 20W/50. That matters because classic Austin Healey engines were designed around older oil specifications and operating conditions, not modern low-viscosity oils intended for newer engines.
Using the wrong oil grade can affect oil pressure, lubrication and protection, particularly when the engine is hot or working hard. If the car has unknown service history, checking what oil is in the engine is a sensible part of hot-running diagnosis.
Oil condition can tell its own story
Oil that smells strongly of fuel, appears badly contaminated or has an unknown age should not be ignored. Over-rich carburetter settings can dilute oil over time, while poor service history can leave the engine relying on oil that has done rather more work than it volunteered for.
Fresh, correct oil will not repair a cooling fault, but it does make the diagnosis cleaner. Once the oil level, grade and condition are known, it becomes easier to judge whether the remaining heat problem belongs to the cooling system, ignition, carburetters or another cause.