The reason for this caution is clear: the distance from his previous posting at the Treasury to Heritage and a Cabinet post is great, demanding a swift gear shift from this clever upwardly mobile politician, who is commonly held to come from the ultra-wet wing of the Tory party, and is beginning to look like its eventual answer to Tony Blair.
There will be one interesting link, though. He has not yet replaced the pictures that his predecessor, Peter Brooke, selected, but he will be bringing a cherished portrait of Oliver Cromwell: 'He is one of the few men who have pushed a political idea so far in one generation.'
In his old job he was associated with two key activities: driving forward the ideological dry policy of market testing, handing over chunks of public sector activity to private contractors (where they were cheaper); and turning up regularly on Newsnight to explain the twists and disasters of government economic policy to Jeremy Paxman.
For Dorrell is that rare creature, a television natural. He says he even likes Paxman and his Rottweiler interview style: 'I always think it's a great deal easier being interviewed by someone who puts you on the spot. I know that's what the viewers want.' Unless an interviewer wants to probe, 'you can't display your best arguments'.
He inherits the White Paper on the BBC, published last month, giving the licence fee a continued if short-term life. He says approvingly that the policy of 'producer choice' introduced by the director-general, John Birt, is in line with the principles adopted by both government and large companies as they strip their operations to deliver accountable, cost-effective services.
During the interview he repeatedly deploys the softish adjective 'bruising' to describe the impact on employees suffering redundancy or new and inferior conditions of work. 'I acknowledge it leads to bruising. It is difficult to reconcile with the desire to be a good employer.'
His new duties at the department custom-designed for David Mellor in 1992 (and quickly nicknamed the 'Ministry of Fun', not a term Dorrell would ever coin) sprawl from sport to high culture. These are not areas in which he claims any great expertise . . . yet. But they offer plenty of scope and no obvious messes to clear up after Brooke's low-key if solid performance. 'I hope I have the interest of an interested layman. I don't pretend to have any special knowledge of the arts, or indeed of sport. But I am interested in developing national expectations and excellence in both fields.' He adds: 'I am interested in ensuring that excellence is available to as wide a section of the community as wishes to avail themselves of it.' Does that mean arts funding is too elitist? 'Look at the objective. The Arts Council has a clear commitment to quality and wide access.'
His limited knowledge of contemporary culture can be attributed in part to limited time. He works hard and lives 'a three-cornered existence': London on weekdays; and weekends shuttling between his Loughborough constituency and Worcestershire home. With his wife, Annette, he has two children, a daughter aged six and son aged one.
'I attend the theatre a few times a year. We go to Stratford, to the Royal Shakespeare Company.' He has 'a fairly complete collection of Elgar's works'. He watches television rarely, on Sunday nights: last Sunday it was Wycliff, ITV's detective drama. Although he used to fly a Tiger Moth, he is not an outdoor man. He laughs at the suggestion he might hunt or shoot. Nor does he talk lovingly of football or cricket. His father, Philip, was a top cricketer, playing as a 'gentleman' for Worcestershire. 'I think I was a disappointment in that area'.
His daily newspaper reading is confined to the Financial Times; no tabloid agenda troubles his life. This springs from his keen interest in business. Before entering politics he worked hard expanding the family firm, which makes workwear. Family wealth cushions his life and seems to free him to concentrate on policies.
He also inherits an unpublished White Paper on privacy and the press. All Dorrell will say on this ticklish subject is that freedom of speech is essential, but that 'there are questions associated with privacy'. He has personally received 'no unfair bruising' from the press; but he is not believed to think highly of all newspaper reporting.
He speaks with enthusiasm about the National Lottery. 'I hope we continue to offer public revenue support (to areas such as the arts). The lottery fund will be complementary, funds essentially for capital projects.' He clearly sees it as a way to hold down public subsidy.
This modern politician is no soft touch. His business background prepares him for thrashing out new cross-media ownership rules, an area in which Labour is breaking much new ground. And here's a tip for the newspaper industry when it goes in to lobby him about press regulation. Take the editor of the FT with you.
STEPHEN DORRELL'S CV
20 July: appointed Secretary of State for National Heritage.
1992-1994: Financial Secretary to the Treasury.
1990-1992: Under-Secretary of State, Department of Health.
MP for Loughborough since 1979.
Views: opposed tougher immigration laws, mocked monetarism, was openly anti-Thatcher.
Special qualities: remembers to say hello to the doormen.