I have been trying to compare 304 stainless steel with 7075 aluminum for some personal research. This steel alloy has a specific heat capacity of 500 J/kg-C, while for aluminum the value is 960 J/kg-C. Does this mean it is harder to heat up aluminum than steel? Then, steel has a thermal conductivity of 130 W/m-K, while for aluminum the value is 16.2 W/m-K. Does this mean that steel conducts heat away better than aluminum? Thank you.
Heat capacity (specific heat) varies inversely with atomic mass, the Dulong–Petit law. Al is about 27 amu, and Fe is about 56 amu, so as you noted, it would be expected that aluminum stores more heat. An extreme example is lead solder, which has such low specific heat that a calloused plumber's hand can wipe a solder joint with little discomfort.
As for thermal conductivity, that property is associated with the rigidity of crystal lattices, where sound travels as phonons, as in diamond, and with electrical conductivity, where "freely moving valence electrons transfer not only electric current but also heat energy." Aluminum and copper are among the best metallic conductors, so are used for cooking-pan bottoms to spread heat evenly. Since stainless steel has many additions to Fe, such as Ni and Cr, these inclusions provide discontinuities at grain boundaries that further impede heat transfer. Dewar flasks are made of stainless steel or glass, rather than Al, because they are poor conductors of heat.