The engine oil requirements for cars from the 1930s to the 1960s have remained very similar (see Chrysler Engine Oil Recommendations for more information). Basically, most cars required a 30 weight oil for normal operation at ambient temperatures above 32°F. In viscosity terms, this means that an engine at operating temperature will require an oil with a viscosity in the range of 9.3 cSt to 12.5 cSt (@ 100°C). Engine oil relies on the oil pan and oil filter for much of its cooling and its operating temperature is affected by ambient temperature as well as the temperature of the engine's cooling water.
Because the viscosity index of older straight oils was relatively low, it was necessary to use lower viscosities with decreasing temperature. For example, a 38 Dodge D-8 (218 I-6) normally required SAE 30 oil in temperatures above 32°F. SAE 40 was recommended for average daily ambient temperatures of 90°F. Oil specifications for 1938-era oils are difficult to find so let's pretend that our SAE 40 oil has a viscosity = 14.4 cSt @ 100°C & VI = 75. We would reach the upper viscosity range (12.5 cSt) for SAE 30 with our SAE 40 oil at about 105°C (221°F) and the lower range (9.3 cSt) at about.117°C (243°F). In other words, modern 30-grade oils (with their higher viscosity indexes) can perform better in extremely hot conditions than the 40-grade oils available when the car was built.
At the other end of the temperature range, the 1938 Dodge required 10W oil at temperatures above 10°F (-12.2°C). Again, oil specifications for 1938-era oils are difficult to find so let's pretend that our SAE 10W oil has a viscosity = 4.1 cSt @ 100°C & VI = 75. We would reach the upper viscosity range (12.5 cSt) for SAE 30 with our 10W oil at about 55.5°C (132°F) in the sump. A modern 10W-30 oil would obviously be able to maintain its viscosity right up to its full operating temperature.