It was hot then, too. My memory of the Labour leadership campaign that unfolded 20 years ago is one of a long, sunny summer in which the candidates often spoke at crowded and sweaty venues, and which culminated in the air-conditioned cool of the auditorium at the Institute for Education near Russell Square.
The same evening, two decades ago tomorrow, I went to the victory party at Church House. The photographs show the mullet-haired young leader on the balcony, grin radiating confidence and modernity. Inside, Blair made a speech that included the words: "Thank you to a friend of mine called Bobby, who some of you will know. He played a great part and did so well." I did not have time to think about it then, because journalists weren't supposed to be at the party and I was being politely thrown out by Tim Allan, one of Blair's early minders. But it remains one of the strangest things Blair has ever said: thanking Peter Mandelson by his codename in front of his supporters, some of whom would have been offended to discover (as they did the next day because the story was in The Guardian) that Mandelson had been secretly working on the campaign all along.
You can tell it was a long time ago. The Daily Mail welcomed his election: "This paper is not in the habit of congratulating leaders of the Labour Party, but then few politicians recently have spoken with the courage and conviction of Mr Tony Blair."
Since then, the Molotov-Ribbentrop Pact of the liberal left and the Mail has worked ceaselessly to poison Blair's reputation, which has continued to suffer since he left office. A whole generation is growing up who know only two things about him: that he "took us into an illegal war" and that he has become rich working for dictators.
Perhaps now would be a good time to remind these young people, who benefited from rigorous teaching of literacy and numeracy in primary schools, that there was a bit more to Blair's record than that. The country has changed, mostly for the better, in 20 years and much of it is because of Tony Blair.
Unexpectedly, the change was best summed up by David Cameron in his words on entering No 10 four years ago, when he said that the country he inherited was "more open at home and more compassionate abroad" than it had been. "Open" is a vague, big-tent word but it describes Blair's legacy well. It covers the public spending after decades of under-investment that rebalanced Thatcherite "private affluence and public squalor". State schools in London went from the worst in the country to the best. The minimum wage. Falling crime. "Open" also covers the greater acceptance of equal rights for women, ethnic minorities and gay people. And it describes Blair's achievement of making the UK, and London in particular, a place where people around the world want to live. London is now the world's most successful global city.
It was notable that when Blair stood down as Prime Minister people told pollsters that the worst part of his record was not Iraq, about which journalists tend to obsess, but immigration. Opening Britain to free movement of EU workers from 2004 helped sustain economic growth and may be part of today's jobs miracle. But it would have been better, looking back, to have adopted the same transitional controls as other EU countries, to slow the disruptive change.
That is the one question on which Blair can still break up the Guardian-Mail Axis. When he gave Ukip what for, on the Today programme the other day, liberal-left commentators were struck dumb by inner conflict as they tried to reconcile the pro-immigration saint with the warmongering sinner.
That wasn't a long struggle, of course. They went back to happily hating Blair for trying to steer General Sisi, Egypt's ruler, in the direction of liberal democracy. Indeed, it seems to have caused them no dissonance that Blair was instrumental in brokering the Egyptian-led ceasefires in Gaza. Fortunately for their world view, Blair has had no more success in bringing peace this time round than he had in securing a two-state settlement in his seven years as Quartet Representative. For the haters, this is proof of his moral failing, not of an impossible task.
The trouble is that, in office, he achieved the near-impossible in Northern Ireland, Kosovo and Sierra Leone. People in those places range in sentiment from the intensely grateful to the taking-for-granted. If Iraq has not gone so well, that was not because his motive was malign.
Twenty years ago, listening in the sunshine to his vacuous rhetoric, I was a bit of a Blair sceptic. Now I look back on his 10 years in office and think that he was, on balance, a good prime minister. For the moment, this opinion marks me out as unusual. In 20 years' time, however, it will be seen for the reasonable assessment that it is.