The ideal gas law states that $PV=nRT$. In many cases you apply this to a closed system with a fixed quantity and volume of gas, so you often see that as temperature ($T$) increases, so does pressure ($P$). A hot air balloon is not sealed or pressurized, however - as the temperature increases, air escapes the balloon. If you consider just the air in the balloon, as $T$ increases, the number of air molecules in the balloon ($n$) decreases, resulting in a system of constant pressure and volume.
Air is forced out by a slight and transient pressure differential. Anytime the pressure in the balloon is higher than outside, air will flow through an opening in the balloon to equalize the pressure. The bigger the pressure differential, the faster air will flow to equalize the pressure, so the internal pressure is always close to (but perhaps slightly higher than) the external pressure, and in an equilibrium state, they are identical.