The phrase "in that summer" is correct and usable in written English.
It can be used to indicate a specific time period in the past, typically the summer season. Example: In that summer, I spent every day at the beach with my friends, soaking up the sun and making unforgettable memories.
His plays have remained infused with "the great transformational myths of our age", as he puts it, and have applied his sharp political analysis to some of the thorniest political issues: the rise of the National Front in Destiny (1980), the human consequences of the miners' strike in That Summer (1987), and the disintegration of eastern Europe in The Shape of the Table and Pentecost (1994).
In that summer of 2010, all Miliband really had was an abstraction – British capitalism rewired for a fairer allocation of wealth and opportunity.
In that summer I watched the Last Poets performing on the back of a truck in a Harlem playground, squeezed into a production of Ed Bullins' Electronic Nigger off Amsterdam Avenue, and queued outside Brooklyn movie houses.
Nothing happened to her in that summer in between.
The couple now live in that summer house, recently insulated on the cheap.
"In that summer when he first came over he was there every day.
"I had joined Richie Barker as player-coach after Alan Durban left for Stoke in that summer of 1978.
But back in August 2011, to my shame, I played a role in that summer of disorder.
("This flat, flourishing, easy country never could have looked more rich and prosperous than in that summer of 1815").
In that summer of 1985, Gooden's 20th victory with the Mets had come at the age of 20 years 9 months 9 days.
For almost everyone who saw "Jaws" advertised on television in that summer of 1975, the chances were good that the film was playing somewhere within driving distance.
