Why wouldn't an accretion disk orbiting a giant star get as hot as an accretion disk orbiting a compact object?
The particles in an accretion disc around a small compact object are moving faster and have more energy.
As with anything orbiting around body, the smaller the orbit the faster the object travels. Particles in an accretion disc around a large star will be travelling relatively slowly
Particles in an accretion disc around a compact objects will be travelling much faster. As a result collisions between particles will have more energy and will generate more heat. Also, gravitational effects from the compact body will provide additional heating effects.