Philip Bowskill, head of Ashfield junior school in Workington, died at home on Tuesday after being taken seriously ill.
Inspectors had been in the school to check its progress after a report last November concluded that the school's management and leadership had "serious weaknesses".
The report blamed Mr Bowskill, 49, for some of the problems, saying he had not led with sufficient vigour and ought to have fewer clerical and administrative duties.
However, sources at the local authority said there was no reason to suspect that Mr Bowskill's death had been linked to the monitoring visit, which Ofsted has postponed indefinitely.
Shocked staff and pupils were told the news of the death in a special assembly before they went home on Tuesday afternoon.
Mr Bowskill, who was married and a father of two, had previously taught at St Bridget's school in Whitehaven. His predecessor there had also died of a heart attack while in service.
In a joint statement, Ashfield school and Cumbria County Council said:
"Philip was a very popular and experienced headteacher and he will be greatly missed by pupils, his colleagues, and the wider school community."