On a hot day, I start to eye keenly the last stations on the Tube and London Overground maps. Richmond, Osterley, Hampton Court and Greenwich beckon. Cobham & Stoke d’Abernon — a Surrey stockbroker station — acquires an appeal it never has in November. The park behind William Morris’s house in Walthamstow will do at a pinch.

London has a population of 8.6 million and is visited by nearly 19 million tourists a year. Where, when the city steams, can you find somewhere cool and secluded?

If I were to dutifully follow the What’s Hot London guides printed in the free magazines handed out on the Tube each morning and evening I would find myself drinking Aperol Spritz on the roof of Frank’s Café in Peckham, queueing for blood-orange sorbet at the Gelupo gelateria in Soho, drinking craft-brewed pale ale at the Brockwell Park Lido, or eating wood-fired pizzas in a narrowboat on a Hackney canal, discarded beer cans bobbing in the water. I would be in the company of several thousand other hot twentysomethings, hot off the hot Tube, having read about the hot destination restaurant, hot off the press.

But I do not want a hot city summer.

There was an architecture professor attached to my university history of art department who lectured on “coolth”. She argued that we all understood what was meant by warmth, that when considering a house, particularly in northern Europe, we sought cosy, cabin-like rooms, gingery colours, curtains to pull against a rainy evening. But why was there no equivalent, commonly-used word “coolth” to describe tiles and terraces, loggias and half-shutters? Her students had T-shirts made up with “COOLTH” printed on the front.

Her campaign for coolth came back to me on a visit to Strawberry Hill in Twickenham on the first Saturday in June. This is the “little play-thing-house” built by Horace Walpole, son of the Prime Minister Sir Robert, in irreverent and anachronistic cod-gothic style. An ogee window here, a turret there, battlements to keep out marauding Twickenham highwaymen, a crinkle of crenellation above the eaves, and a quatrefoil window or candy-cane chimney wherever the elevation is in danger of looking even half sensible. It was at Strawberry Hill that Walpole dreamt of a giant disembodied hand in armour hovering above the bannisters of a great staircase, an apparition which inspired his 1764 novel of sensation The Castle of Otranto.

He wished, he wrote in one letter, to imprint the “gloomth” of abbeys and cathedrals on his summer cottage. The word, like coolth, has not been widely taken up. “Application peculiar to Walpole,” says the OED.

One could have too much gloomth, though. “One’s garden,” Walpole continued in the same letter, “on the contrary is to be nothing but ‘riant’, and the gaiety of nature.”

It was riant when we visited with a picnic and a Pevsner. Riant enough to have sunburnt forearms and cheeks from an afternoon sitting on the lawn below Walpole’s oriel windows. (“Fanciful and unarchaeological,” says my 1951 Pevsner’s Buildings of Britain: Middlesex.)

We had the garden, which to borrow from Walpole was “in the height of its greenth, blueth . . . honeysuckle and seringahood”, almost to ourselves. A group of children were peaceably bug-hunting in the long grass. I would not have been at the Brockwell Park Lido for all the craft ale in London.

The gloomth of Walpole’s entrance hall after the wedding-cake white of the house takes a moment’s getting used to. Not since the days of Abelard, Walpole wrote, had a room been so venerably gloomy. It is just the place on a hot afternoon.