Think about these over a cup of coffee

Image stolen from the execellent comic: Too Much Coffee Man

If you drink your coffee black, the way god intended, you may skip this problem.

Every morning, my brother Jim drives to the bagel shop the get his common law wife, Natalie, a hot coffee. Natalie likes milk in her coffee. If Jim wants to give Nat the hottest cup of coffee he can, when should he add the Milk? Should he add it at the shop, or should he wait until he drives home and add the milk from the fridge? Make all the standard reasonable assumptions...

Waiter, there's a cardioid in my coffee...

One sunny day last summer, my brother Russ sat outside and drank coffee. He looked into the cup, and reflected on the surface of the coffee was a sharp outline of what looked like the top of a valintine's day heart. Explain how this shape appears.