Despite a reputation as a shadowy, opaque figure, records show him able to argue shrewdly and independently in order to reduce problems for the Crown.

[4] Heath brought a 1625 case in the Exchequer Court for the High Peak lead miners against Francis Leke who claimed a tithe from them.

From 1629 he was taking an entrepreneurial interest in the lead mines of Derbyshire, engaging Sir Cornelius Vermuyden as a partner in a major drainage operation at Wirksworth, at the ore-rich Dovegang Rake.

The judges rejected his argument on absolute prerogative; and a scandal blighted his reputation the following year, when it was revealed, or alleged, by John Selden that he had interfered with the King's Bench records (a felony), in order to promote the decision in the case to a binding precedent (an interpretation that has recently been disputed by Mark Kishlansky).

On the other hand, this is not accepted by Thomas G. Barnes, who argues that Heath with Sir Richard Shelton had displeased the King, and on an old matter: plantations in Ulster and the obligations of the City of London in an agreement made under James I, as interpreted in a lax fashion by the law officers of the Crown (Heath as Attorney General, Shelton as Solicitor General).

His reputation as pro-Puritan, anti-Laudian did him no harm with the Long Parliament when Charles brought him back as a judge, making him Lord Chief Justice.

A year later, Sir John Berkeley, the royalist Governor of Exeter, carried out the death sentence on Turpin, as retaliation for the hanging of a Parliamentary commander who had defected to the King.