In this study, thyroid cancer incidence (follow-up period: 1991-2001) has been analyzed, including persons who were exposed as children at an age between 0 and 17 years and who are living in the Bryansk oblast, the worst contaminated area of Russia after the Chernobyl accident. According to the census of 1989, the population of this oblast comprises 375 thousand people. Thyroid doses from incorporated radioiodine isotopes -- both for the thyroid cancer cases and the study population -- were determined based on the official methodology approved by the Russian Scientific Commission on Radiation Protection. Between 1991 and 2001, a total of 199 thyroid cancer cases were diagnosed at cancer centers (the so-called oncological dispensaries) of the investigated regions. The performed analysis relies on medical and dosimetric information available from the Russian National Medical and Dosimetric Registry which was established after the Chernobyl accident. Diagnoses were confirmed histologically for 95% of the cases. The analysis described revealed statistically significant radiation risk only for those exposed as children at an age of 0-9 years. In this group, the standardized incidence ratio (the national incidence rate was used as a reference) in the considered time period is estimated to be 6.7 (5.1, 8.6 95%CI) and 14.6 (10.3, 20.2 95%CI) for girls and boys, respectively. The risk dependence on age at exposure has also been studied. It has been shown that the smaller the age the higher the risk. For girls whose age at exposure was 0-4 years, the excess relative risk per 1 Gy for the period 1991-2001 was 45.3 (5.2, 9,953 95%CI; with internal control) and 28.8 (4.3, 2,238 95%CI; with external control), respectively. For boys whose age at exposure was 0-9 years the corresponding excess relative risk per 1 Gy was 68.6 (10.0, 4,520 95%CI) and 177.4 (-276, 10(6) 95%CI), respectively. Dependence of radiation risk on time was studied, with the focus on two follow-up periods 1991-1996 and 1997-2001, respectively. In 1997-2001 the radiation risk is shown to decrease among girls, and increase among boys.