Is it because of James Madisons urging, the election of 1800 was finally settled? or was it someone else?

Question

Election of 1800

Connecticut, Delaware, Georgia, Kentucky, Maryland, Massachusetts, New Hampshire

New Jersey, New York, North Carolina, Pennsylvania, Rhode Island, Tennessee,

South Carolina, Vermont, Virginia

Candidates Thomas Jefferson Aaron Burr John Adams

Political Party Democratic-Republican Democratic-Republican Federalist

Electoral Vote 73 73 65

States 8 8 7

House Run-Off 10 4 -

Adams in the end gave the election to Jefferson, who had tied with Burr.

so it's Thomas Jefferson correct?

No, Adams settled it. See the last sentence.