As a senior at Torrance High School in Torrance, California, Thompson scored 30 or more points five times and had 20 or more rebounds on six occasions, and led his team to the Division II-A finals in 2006 and quarterfinals in 2005. He averaged 21.5 points, 13.8 rebounds and 4.6 blocked shots as a senior. Thompson wore number 21 for North Carolina; when his college career ended in 2010, he had played in a total of 152 games, at that time the most in NCAA Division I men's history.
Professional career
After going undrafted in the 2010 NBA draft, Thompson joined the Minnesota Timberwolves for the 2010 NBA Summer League. On August 1, 2010, he signed with Greek club Ikaros Kallitheas for the 2010–11 season. On July 20, 2011, Thompson signed a two-year deal with Slovenian club Union Olimpija. With Olimpija he won the 2012 Slovenian Cup. On August 7, 2012, he parted ways with Olimpija. On August 12, 2012, Thompson signed with German club Alba Berlin for the 2012–13 season. With Alba he won the 2013 German Cup. At the end of the season he was named to the All-BBL First Team. On August 2, 2013, Thompson signed with Bayern Munich. With Bayern he won the 2013–14 Bundesliga, and was also named to the All-BBL Second Team. On August 14, 2014, he parted ways with Bayern. On August 26, 2014, Thompson signed with the Liaoning Flying Leopards of China for the 2014–15 CBA season. On March 23, 2015, he signed with Hapoel Jerusalem of the Israeli Premier League for the rest of the season. On July 20, 2015, Thompson returned to Bayern Munich, signing a one-year deal. On July 12, 2016, Thompson signed with Galatasaray for the 2016–17 season. On January 2, 2017, he left Galatasaray and signed with Serbian club Crvena zvezda for the rest of the season. On August 19, 2017, Thompson signed with Spanish club San Pablo Burgos and became the top rebounder of the 2017–18 ACB season with 6.7 rebounds per game. He was also named MVP of the week after performing and average index of 31 in the club wins at MoraBanc Andorra and versus Real Betis Energía Plus. On August 6, 2018, Thompson re-signed for one season with Spanish club San Pablo Burgos. On January 6, 2019, Thompson left Burgos and signed with Lithuanian Žalgiris Kaunas until the end of the season. He helped Žalgiris reach the EuroLeague playoffs, and win the Lithuanian Basketball League championship.