We have developed the tunable dispersion compensator based on two twin linearly chirped fiber Bragg gratings with various temperature gradients. Controlling the temperature gradient over one of the twin fiber Bragg gratings by Peltier elements, the dispersion and the dispersion slope were changed independently and continuously. The dispersion and dispersion slope compensator has a large bandwidth of 8 nm and low group-delay ripple of < 4 ps in its chirped fiber Bragg gratings. We experimentally demonstrated a precise controllability of the dispersion and the dispersion slope using linear and parabolic temperature gradient. The dispersion and the dispersion slope changes were achieved continuously with -0.67 ps/nm/ and -0.14 ps/nm2/. The transmission characteristics of the dispersion slope compensation were examined using ultra short pulses in the fiber link. When the total dispersion was zero, the distorted pulse was restored back and the tail was significantly suppressed. 160 Gbit/s signals were also demonstrated over 140 km within 1 dB power penalty by using the dispersion slope compensator.