This could be surprising to a lot of people, but modern central banks, including the Fed, can't control the quantity of money and the interest rate at the same time.
Controlling one means losing the control of the other and modern central banks control the interest rate, not the quantity of money.
So, the causality is like this: when the economy gets hot, more credits are asked by business and households, because of that, the interest rate go up. In order to keep the interest rate in their choose target, central banks will add more money to the system. The Fed doesn't decide the quantity of money, the economy does it.
Controlling one means losing the control of the other and modern central banks control the interest rate, not the quantity of money.
So, the causality is like this: when the economy gets hot, more credits are asked by business and households, because of that, the interest rate go up. In order to keep the interest rate in their choose target, central banks will add more money to the system. The Fed doesn't decide the quantity of money, the economy does it.