The rotund Jackie Gleason, who died Wednesday, sweltered through the summer heat in Phoenix, but his old friend Tom Chauncey said ''The Great One'' didn't let the heat slow him down.

Chauncey, the former owner of KOOL-TV (now KTSP-TV) said Wednesday night that he was contacted by CBS in 1962 and was told that Gleason would be coming through Phoenix on a leased Santa Fe train.

It was the last ride of the Gleason Special.

''He had just finished making the movie Papa's Delicate Condition, and he came through here with the June Taylor Dancers and Sammy Spear and his orchestra.

''There were all kinds of people on that train. I remember that the women were beautiful, but well-chaperoned by June Taylor,'' he said.

''I didn't know exactly how to entertain Jackie, so I built a small bar over at the station and called it 'Toots Shorr's.' He spent a lot of time at that bar, but I never saw him drunk.''

Chauncey said there were a lot of people who wanted to meet Gleason and he figured the best way to accommodate everyone was to host a luncheon for 400 to 500 people at the Westward Ho Hotel.

''Wayne Newton had sung at the station, and I knew him so I called him in Las Vegas and asked if he could come down here and sing for a luncheon I was throwing.

''I didn't tell Wayne that the guest of honor was Jackie Gleason.

''Wayne and his troupe were doing six shows a day in Vegas, but they got off in the middle of the night and drove down here.

''When Jackie heard Wayne he just loved him. He immediately hired him to sing in his next three shows. Jackie really got Wayne's show business career going.''

Chauncey said Gleason had just about decided to move to Scottsdale in 1964, but that Florida decided to recruit him to live in that state.

''They offered him the moon,'' Chauncey said. ''Jackie wanted to live in a climate where he could play golf year-round so the city of Miami Beach built him a home overlooking the fairway of Miami Beach Country Club.''

Chauncey said he visited Gleason many times after that first meeting in 1962 and the two of them became good friends.

''He was kind to everyone. He was just a very good man.

''Like I said before. He drank a lot but no one ever knew it because he just didn't get drunk. He was always a gentleman.

''I'm very sad that Jackie's gone. Somewhere around here I have a picture of us together. I'm going to have to find it.

''It was taken when he got off that train on that terribly hot day. Jackie was wearing a jacket and that silly hat.''