We describe a method for precisely controlling temperature using a Gifford-McMahon (GM) cryocooler that involves inserting fiber-reinforced-plastic dampers into a conventional cryosystem. Temperature fluctuations in a GM cryocooler without a large heat bath or a stainless-steel damper at 4.2 K are typically of the order of 200 mK. It is particularly difficult to control the temperature of a GM cryocooler at low temperatures. The fiber-reinforced-plastic dampers enabled us to dramatically reduce temperature fluctuations at low temperatures. A standard deviation of the temperature fluctuations of 0.21 mK could be achieved when the temperature was controlled at 4.200 0 K using a feedback temperature control system with two heaters. Adding the dampers increased the minimum achievable temperature from 3.2 to 3.3 K. Precise temperature control between 4.200 0 and 300.000 K was attained using the GM cryocooler, and the standard deviation of the temperature fluctuations was less than 1.2 mK even at 300 K. This technique makes it possible to control and stabilize the temperature using a GM cryocooler.