One thing I will always remember is when in 2006, the Republicans brought Kerry/Feingold, a resolution for leaving Iraq to the floor. The Democratic leadership did not want this issue debated as the centrist wing of the party, including the Clintons and Harry Reid, were of the opinion that debating leaving Iraq would hurt the Democrats in 2006. As a result, people like Joe Lieberman, who lied about it and trashed it and the two Senators were given the prime slots to speak.
When John Kerry, rather late at night, spoke he spoke of how there had been no real debate on the ideas included. John Warner, who was then the Chair of Armed Services, asked Kerry if he could engage him in a debate. Kerry accepted. Warner spoke of how there were many good, thoughtful ideas, but that he did not think it was yet time. He then went on a tangent to say that he was Secretary of teh Navy when Kerry was in Vietnam and that he had personally reviewed his silver star and bronze star with valor - and then said they were well deserved. The two men then debated the provisions of the resolution. (I spent a lot of time in DU JK then and it was a common view that Warner had treated Kerry with more respect than many of his Democratic peers - even as they disagreed One result was Warner took one part, a regional summit to help Iraq go forward into the defense bill - though it never actually was implemented. )
In the years since he was in office, his name was on many national security letters (against Trump actions) and supporting many climate change actions.