It starts with a town that was hit by a mysterious explosion which transports that town into a desert. The weather is cold and people burn coal but they soon run out and send out an expedition to look for signs of life - they navigate the desert for a couple of days and come across a glass dome covering a city. Apparently they have been transported far in the future.
And that's where I stopped reading and want to resume now. Don't remember the title or the author and it's at least 20 years old.
City at World's End, a novel by Edmond Hamilton; originally published (with "The" in the title, and possibly in a shorter version) in Startling Stories, July 1950, which is available at the Internet Archive. There is a reading at LibriVox.org. Maybe one of these covers will ring a bell.
It was then that Kenniston realized the other wasn't looking down at the town but out beyond it. He too looked.
He didn't get it at first. He didn’t get it at all. He thought it was an illusion created by the strange dusky-red sunlight.
There should have been flat green smiling farmlands out there around the town—the flat lands of the Middle West.
But that was all gone. It was a completely different countryside that now lay around Middletown.
Ocher rolling plains stretched wanly under the dusky red Sun toward low hills that had never been there before.
The river was gone. There was nothing but the dull yellowish vegetation and the distant hills.
The wind blew over the barren world out there and stirred little clouds of dust that fell back again to earth. The Sun glared down like a great dull-red eye with lashes of writhing fire and the glimmering stars swung solemn in the dusky sky.
Kenniston’s shocked mind frantically sought explanation for that impossible scene.
"Then the bomb somehow devastated the countryside instead of Middletown?"
"Would it take away a river and bring in its place those hills and that ocher vegetation?" Hubble said. "Would the bomb do that?"
"But then, what—?"
"It hit us, Kenniston. The bomb hit Middletown. It went off right over us and it did something queer to us.
"Nobody really knew what a super-atomic would do when it went off. There were logical theories and assumptions about it but nobody really knew anything except that the most violent concentrated force in history would be suddenly released.
"It was released, over Middletown. And it was violent. So violent that it ripped a hole in the continuum itself—the space-time frame of our cosmos.
"And we were flung through that hole, Kenniston. Middletown was flung through."
Kenniston stared blankly. "Flung through into what?"
"Into another part of the continuum, Kenniston. Into another part of the space-time frame."
Hubble gestured with a shaking hand. "That’s our Sun but it is old now—very old. And the Earth out there now is an old Earth. And the stars—
"You looked at the stars, Kenniston, but you didn't see them. They're different. The constellations are distorted as only millions of years of time could distort them."
"Millions of years?" It was Kenniston who whispered now.
"Yes. The Sun is old and Earth is dying, almost dead. And we, all of us and our little city, have been flung through into this far future of twilight and death."
