In the letter, children from class 12c at the Ludwig-Meyn high school in Uetersen, near Hamburg, reminded Boetticher of a "heated discussion" he was involved in six months ago.
"You defended the position of your party: that a 16-year-old is so far behind an adult in both maturity and education that he or she cannot make responsible political judgements," the letter said.
The teenagers said the revelations about Boetticher's affair with a 16-year-old "put the whole discussion in a new light."
"You fell in love with the intelligent and enriching political opinions of someone in our age group," they said. They are now calling on Boetticher to become a supporter of their campaign to lower the voting age in Schleswig-Holstein to 16.
The 40-year-old Boetticher has made no response to the letter. A spokesman said he was ill and is currently not making public statements.
The scandal surrounding Boetticher's brief affair with a 16-year-old cost him the CDU party leadership in Schleswig-Holstein, as well as the candidacy for the state premiership in next May's election.
The couple met on Facebook early in 2010 and began an affair which Boetticher broke off in attempt to protect his career after a few months. In his tearful resignation speech on August 14, Boetticher said it had been a serious love affair.
He said he was stepping down to prevent his party from political damage, "but in particular to protect beloved people in my private life."
Boetticher said the girl, a member of the CDU's youth organization Junge Union, had caught his attention with her "very intelligent" comments on his Facebook updates.
He said she was "intellectually very mature for her age," and he was able to "communicate with her on the same level."