No official cause of death has yet been revealed, with Pervez Mir, the Pakistan team's media manager, saying on Monday: "We are waiting for medical reports."
But according to reports, Woolmer suffered from diabetes and had recently experienced breathing difficulties.
On Sunday protesters in the city of Multan had shouted slogans against him and Inzamam-ul-Haq, the national team's captain, while others in Hyderabad city reportedly held mock burials for the team.
But by Monday supporters had changed their tune and were saying that Woolmer's huge commitment - and his disappointment about the team's World Cup failure - may have led to his death.
Pervez Musharraf, the president, and Shaukat Aziz, the prime minister, led tributes to him late on Sunday.
The foreign ministry followed on Monday, saying it was "very sad that he died after a very poor performance by the team, and his life didn't end on a happy note".
Nasim Ashraf, the Pakistan Cricket Board chairman, said Woolmer had "always termed Pakistan as his home."
1975: Test debut for England
1975: Voted Wisden cricketer of the year
1981: Played last test for England
Highest score: 149
1991: Becomes director of coaching at Warwickshire.
1993: Warwickshire win NatWest Trophy.
1994: Warwickshire win three out of four trophies and are runners up in the NatWest series. Appointed coach of South Africa.
1999: Leaves South Africa job after team fails to make World Cup final
2001: Joins ICC as high performance manager.
2004: Announced as new coach of Pakistan
Speaking to the UK newspaper Daily Mirror, Gill, Woolmer's widow, revealed the pressures placed on her husband as coach of the cricket-mad Pakistan.
"His job coaching there has been incredibly stressful," she said.
Javed Miandad, the former Pakistan captain whom Woolmer replaced as coach in 2004, said he believed "Pakistan's shock defeat against Ireland had a lot to do with his death."
Asif Iqbal, another former Pakistan captain, agreed.
Private television channels, for their part, erased vitriolic text messages left by viewers on Sunday before news of Woolmer's death had come through.
"We have deleted all the earlier SMS and public reaction, after Woolmer's death," Ather Viqar Azeem, a producer for a sports programme on HUM TV, said.
Woolmer was largely treated with goodwill in the cricket-obsessed Muslim nation of 150 million people, despite concerns about having a foreign coach.
British newspapers on Monday called him a garrulous "citizen of world cricket" whose pioneering career as a coach was brought to an end by a cruel twist of fate.
|Woolmer was a former England batsman|
and Warwickshire coach [AFP]
His use of computer technology to pinpoint players' weak spots and his cheerful character were the hallmarks of his approach to the game, the Daily Telegraph
But these qualities were "tested to the limit by his last seven months in charge of the Pakistan team, which lurched from one crisis to another", the paper said.
These included the now-notorious match last September in England when umpire Darrell Hair's decision to dock Pakistan five runs for ball-tampering triggered a sit-in by the team.
The following month, fast bowlers Shoaib Akhtar and Mohammad Asif failed drugs tests, although later had their bans overturned on appeal.
Despite such difficulties, Woolmer was able to discipline the team, the Times said.