Material in an accretion disk heats up due to friction within the disk. The basic answer to your question is that the closer you get to a massive object, the more heating occurs, and the hotter the disk gets. Since you can get closer to a black hole (or other compact object, such as a neutron star) than you can to a giant star, accretion disks around compact objects are hotter.
The way to think about this in detail is to imagine each particle in the accretion disk in orbit around the massive object in the center. Closer to the massive object, the force of gravity will be stronger so the particles there get pulled around in faster orbits than the particles which are further away. Therefore, if you imagine two adjacent "rings" of particles centered on the massive object, the ring that is closer to the massive object will be spinning around faster and so it will rub against the ring next to it.
This rubbing between the two "rings" will heat them up due to friction between them. The rate at which heat is generated from this process depends on several factors - for example, how strong the friction is between the two rings. If the accretion disk is made up of material that is very viscous, it will heat up more. As a silly example to make things clear, an imaginary accretion disk made of molasses would heat up more than an imaginary accretion disk made of water! In fact, the source of the viscosity in the material that actually does make up an accretion disk is thought to be due to mixing by turbulent magnetic fields (so it isn't really a "viscosity," technically speaking, although it works in a similar way).
However, for our purposes we don't have to worry about the viscosity - the effect that we really care about is the relative speed of the two rings rubbing against each other. As you can imagine, if the rings are rotating faster with respect to each other, they will "rub" against each other more and generate more heat.
Now, it turns out that the closer you get to a massive object, the greater the relative speeds between two adjacent rings of particles orbiting the object. (To see this, you might need to use a little math. The force of gravity from a massive object is proportional to 1/R2, where R is how far you are from the object. If you play around with some numbers you can see that if R is small, changing R by a little bit will give you a big difference in the gravitational force. That means that if you are very close to the massive object, the gravitational force on two adjacent rings will be very different, so the inner ring will get pulled around in a much faster orbit than the outer ring, and the relative speed between the rings will be larger than the relative speed between two adjacent rings further out.)
So what does this all have to do with the difference between giant stars and compact objects? Simply that with a giant star, the accretion disk can't get very close to the center of mass! If you try to get too close, you will suddenly find yourself hitting the surface of the star and entering into it. But if you imagine a compact object of the same mass as the giant star, then by definition it is a lot smaller so you can have an accretion disk extending much closer to the object's center. In the inner part of this accretion disk, the "rings" of material will be rubbing against each other very hard, so this part of the accretion disk will get very hot.
This page updated on June 27, 2015