Cote previously worked for General Electric[3] and TRW Inc.[4] before he was appointed chairman and chief executive officer (CEO) of Honeywell in 2002,[4] following their acquisition by AlliedSignal.

Cote also sat on the JP Morgan Chase risk committee during the period in which the firm lost $6 billion trading credit derivatives.

[6] The following year, Cote enrolled at the University of New Hampshire,[3] and while attending UNH full-time, he worked an hourly job on the night shift at a nearby GE jet engine plant.

[3] Over his career there, he held positions in manufacturing, finance, marketing, strategic planning and general management,[7] before becoming CEO of GE Appliances in 1996.

[7] In November 1999, Cote joined TRW as president and COO where he introduced the Six Sigma management system to reduce defects in manufacturing.

In an effort to reduce the unpredictability of asbestos-plus-environmental expenses, Honeywell established a trust for claims and reclaim soil at chemical plants.

[3][15] While CEO of Honeywell International in 2015, Cote earned a total compensation of US$25,053,000 which included a base salary of $1,890,000, an annual bonus of $5,700,000, and $10,338,000 in stock options.

In 2012, Cote came under criticism as one of the three members of JP Morgan Chase's risk committee, after CEO Jamie Dimon said on May 10, 2012, that the firm's chief investment office suffered a $2 billion loss trading credit derivatives.

[32] Cote is a co-founder of Fix the Debt, a group of executives and former legislators who campaign for deficit reduction and tax reform.

In a 2013 interview with the New Hampshire Union Leader, Cote identified the problem of debt reduction in the United States as being the fact that "Washington is ruled by fear of voters ... and the three 'h's' prevail—hysteria, histrionics and hyperbole".