Specific heat = ratio of the quantity of heat that we require to raise the temperature of a body by one degree compared to doing the same of an equivalent mass of water.
Also, we use the term in a narrower sense to mean the amount of heat, in calories that we require to raise the temperature of one gram of a substance by one Celsius degree.
Q = m * c * ΔT,
c = specific heat, units of J / (kg * k), (k = kelvin) Q = heat energy, in Joules ... or "transfer of heat"
combining masses with different temperatures:
tf = (m1*c1*t1 + m2*c2*t2 + ... ) / (m1*c1 + m2*c2 + ...) tf = temperature final (see https://www.engineeringtoolbox.com/temperature-mixing-liquid-solids-d_1754.html)
Thermal conductivity K in watts/(meter * kelvin):
K = (Q * d) / (A * delta T) A= surface area, in square meters d = distance between planes / thickness of material
rate of heat conduction = Q/t
Q/t = (K * A * deltaT) / L A = area of cross section, L = length of material K = thermal conductivity
For two materials that are joined, see the temp at the middle by setting Q/t of one item to another (see https://physics.gurumuda.net/heat-transfer-conduction-problems-and-solutions.htm)