I recently purchased some slaked lime online and suspect it is not good (not fully slaked?).

When added to water around 35 °C, it heats to about 80 °C. My understanding is that slaked lime should not have this reaction and I am therefore guessing there is still some quicklime remaining in it somehow. Is this correct, or is it normal for even slaked lime to heat so dramatically?

You also misunderstand about quicklime. Quicklime is Calcium oxide, $\ce{CaO}$. It is formed by heating calcium carbonate and driving off carbon dioxide. Quicklime is reacted with water to form calcium hydroxide so that the quicklime, which has now cooled, won't react with carbon dioxide in the atmosphere to form calcium carbonate again.