WASHINGTON — The moment President Trump left Washington aboard Air Force One on Friday, bound for the New Jersey golf course where he will spend his summer vacation, a White House employee switched off the air-conditioning in the West Wing to turn the area officially into a construction zone.

By then, senior White House officials — including Mr. Trump’s chief of staff, top advisers, lawyers and spokespeople — had already cleared out to decamp to the Eisenhower Executive Office Building next door.

That French Second Empire-style building will be their temporary office while government workers undertake a major West Wing renovation — a roughly two-week, $3.4 million overhaul that includes replacing the air-conditioning and heating system and installing new cables and wires, fresh paint and new carpets.

Mr. Trump’s departure from the steamy capital marked the start of the project, and a handy excuse for the president to escape northward to the relatively cooler temperatures of his Bedminster, N.J., property.