However, disinformation could yet render calculations inaccurate as they did when Mrs Thatcher unexpectedly worsted Edward Heath in 1975.
Most MPs kept their heads below the media parapet, but ardent partisans on both sides insisted their candidate would win the first ballot, except when it suited them to tell susceptible colleagues that their opponent would do so in the hope of alarming waverers.
'It's slipping away from her,' predicted one Midlands veteran who will be voting for Mrs Thatcher in the first round. Neither her flirtation with a referendum on European currency policy, nor accusations in press interviews that Mr Heseltine is a crypto-socialist 'interventionism, corporatism, everything that pulled us down' were thought to have done her much good.
The corridors of Westminster were suddenly calm after a frantic week. In contrast to the soothing tactics of the Heseltine camp, Norman Tebbit and Nicholas Ridley raised the temperature on the airwaves.
Constituency activists were reported to be solidly behind the leader another echo of 1975. 'It shows a certain anxiety,' said one dissident, Sir Philip Goodhart.
Mr Heseltine protested that he had been regarded as 'rather a good egg' when he was at the cutting edge of privatisation before his resignation from the Cabinet in 1986. He rammed home his message that electing him was the only way to protect Thatcherism's achievements from a Labour government. Sentiment in the City also seemed to be moving towards a change.
Mr Heseltine is privately confident that he has done well enough to force a second ballot in a week's time. He rounded off his run with a polished performance on BBC TV's Panorama which included an appeal for unity whoever wins. He had campaigned with 'no bitterness, no hype of language, no temperament', he said.
One of his advisers contrasted the Thatcher campaign's mixture of aggression and apparent invisibility with the quip: 'Why are we doing so much better? Their people are lying like troopers. Ours are lying like officers.'
At her two Paris summit press conferences, including one with President Bush, Mrs Thatcher was deluged with questions about the leadership.
'I most earnestly believe I'll be there a little bit longer,' she said at one point, subdued but steady under fire. At another she said she hoped to be remembered for more than the day's historic arms control agreement. 'It's not time to write my memoirs yet.'
If Mrs Thatcher 's declared optimism is misplaced, she could go quickly or struggle to survive until a renewed crisis next spring. Strong mistrust of Mr Heseltine, which the campaign has revealed, may force Tory grandees to seek a quick decision which the City would also favour.
If fewer than 200 of the 372 available votes are cast for the Prime Minister the minimum figure claimed by loyalists last night the result will be widely seen as fatal to her.
That judgment may stick even if a crucial block of abstentions brings what is technically outright victory on the first ballot 56 votes clear of the former Defence Secretary. If there are more than 250 Thatcher votes, then it is Mr Heseltine who will have suffered the serious rebuff.
But if voting falls in the grey area in between, many MPs believe the party establishment, the 1922 committee executive and grandees like Lord Whitelaw, would press the Prime Minister to step down. That would enable a 'Stop Michael' candidate, most probably Douglas Hurd, the Foreign Secretary, but possibly John Major, the Chancellor, to enter the race. Nominations would have to be submitted by Thursday.
Today's voting, which will culminate in a rapid count at 6pm, ends a seven-day contest which was becoming increasingly acrimonious within Mrs Thatcher 's praetorian guardsmen.
Most conspicuously, the former party chairman, Mr Tebbit, created a small photo opportunity outside the challenger's London house to report that the Prime Minister was in good heart. 'What do you expect from the woman who sorted out Arthur Scargill, General Galtieri, and is now standing up to Saddam Hussein?' he pointedly asked.
The former Trade Secretary, Mr Ridley, attacked Mr Heseltine's Europeanism. He said: 'If Mr Heseltine ever were to be Prime Minister and were to seek to join a single currency, he would lose among 60 to 70 per cent of the Conservative Party in the House of Commons.'
The challenger himself was as affable as he has remained throughout, presenting himself as acting more in sorrow than anger. On BBC Radio's World at One he responded blandly to Mrs Thatcher 's counter attacks that his views were 'more akin to some of the Labour Party's policies'.
Mrs Thatcher may have taken the credit, he said, but it had been a team effort which she led. His own success on council house privatisation had made further sales to the private sector possible, instead of merely 'managing the state more effectively', as the 1979 manifesto had promised.
In Paris, Mrs Thatcher also stressed teamwork and said she would still be in Downing Street at the weekend. 'What makes me so confident is that I have a marvellous team working with me and I think we are all very optimistic,' she said.
President Bush declared: 'I stay out of all this,' but he ventured a testimonial to his 'superb relationship' with the Prime Minister.