Plain carbon steel is an alloy of iron and carbon.
(Other elements like manganese, silicon, copper are also allowed in carbon steel but with low maximum percentages.)
On the other hand stainless steel is an alloy made up of steel mixed with elements such as chromium, nickel, molybdenum, silicon, aluminum, and carbon.
From the foregoing we see that stainless steel has higher concentration of alloying elements as compared to plain carbon steel. Free electrons which are involved in thermal transport process in metals experience more scatterings from atoms of alloying elements in stainless steel. This leads to poor thermal conductivity of stainless steel in comparison to plain carbon steel.