The first woman to be elected to lead one of Britain's main political parties was delighted with her reception in Scotland. "I have been given the most marvellous welcome that any politician could ever have been given anywhere in the world," she told a lunch for 600 party officials, MPs and supporters later in the day.
The St James Centre – later to be dubbed Edinburgh's ugliest building – may seem a curious venue for Mrs Thatcher's Scottish debut. But back in 1975 it was new and shiny, rather like Mrs Thatcher herself.
And just as people now find it incredible that such a development was ever given planning permission, some Scots might find it difficult to believe there was ever that kind of welcome north of the border for the woman who would later introduce the poll tax, close the mines and be accused of destroying Scotland's traditional industries.
Edinburgh Pentlands MSP David McLetchie recalls a "tremendous enthusiasm" for Mrs Thatcher in those early days. "She had a bit of the Obama effect because of the sheer novelty of it at that time," he says. "I remember her visits and speeches at conferences. There was a real passion and enthusiasm. She says herself in her books that the atmosphere was terrific."
Mrs Thatcher's election victory in 1979 – 30 years ago on Sunday – followed a vote of no confidence in James Callaghan's Labour government a few weeks earlier. The country had come through the Winter of Discontent and seen the failure of the referendum for a Scottish Assembly.
The Tories got in with a majority of 43 over all other parties. In Scotland, they took 31 per cent of the vote and won 22 of the 71 seats. It was a better performance than the previous election, but mainly thanks to the collapse of the SNP, which went from 11 MPs to just two.
In Edinburgh, the Tories already held four out of the seven parliamentary seats and the party's vote increased in most constituencies across the city.
David McLetchie – who was the Tory candidate against the late Robin Cook in Edinburgh Central in 1979, his one and only bid for election until he stood for the Scottish Parliament in 1999 – says Mrs Thatcher was an unknown quantity in Scotland at the time.
"She was an English MP and in the previous Tory government she had been Education Secretary, which meant she did not have direct dealings with Scotland."
He says Mrs Thatcher maintained her popularity in Scotland over the first four years of her government. In the 1983 general election, the Tories lost just one seat.
But after that, he says, unemployment and the change in Scotland's industrial base gathered pace. In the 1987 election, the party collapsed from 21 MPs to just ten. And after winning one seat back in 1992, it went on to lose all its Scottish MPs in Labour's 1997 landslide.
Mr McLetchie refuses to blame Mrs Thatcher for the party's decline, although he accepts her initial popularity in Scotland turned to something much more negative. "Her persona and image didn't play well for large sections of middle Scotland in the same way as she had a strong appeal in England.
"She became a figure that could readily be demonised and caricatured by our political opponents. Sometimes Mrs Thatcher had a harder image than her policies actually warranted and she played up to the caricature. Instead of showing a more compassionate and sympathetic tone – which I think was there – she almost lived up to her image and felt she had to be the strident Iron Lady."
Mr McLetchie insists the poll tax, introduced a year early in Scotland, was not the Tories' nemesis. "The wipe-out in 1997 was as much to do with the failings of the Major government as anything Mrs Thatcher had done."
He admits there is still a "perception problem" for the Tories in Scotland because of the negative memories of Mrs Thatcher. But he would rather reclaim her legacy than try to disown it. "We should celebrate her achievements," he says.
That's not a universal feeling in the party, however. The Tories in Scotland have been much slower to recover than the party down south. And even if David Cameron becomes Prime Minister at the next election, no-one expects him to have more than a handful of Scottish MPs.
Even after all these years, for many Scottish voters, mention of the Tories brings to mind Mrs Thatcher's apparently "anti-Scottish" policies – the injustices of the poll tax, the bitterness of the miners' dispute and the willingness to let once proud industries go to the wall.
In an interview for a new book about Mrs Thatcher and Scotland by former Evening News journalist David Torrance, the former Prime Minister does little to alter such perceptions, accusing Scots of being in "self denial" about their "culture of dependency".
Lady Thatcher herself will attend a dinner in Glasgow on Saturday to mark the 30th anniversary. But some senior Scottish Tories believe the occasion will simply dredge up memories and revive hostility to the party.
"The anniversary could not be ignored," says one party insider. "But it's never going to be a happy story."