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I read a paperback in the mid-1970's in which combatants fought a war using time travel and adaptive computers. After a battle, the victors had to quickly flee because the opponents would return from the future with superior technology.

In one case the victors failed to flee before coming under an attack from the future. There was a reluctant, last-resort defense using a massively explosive weapon, like an A-bomb, from which the earlier-time combatants were shielded by a force field.

I recall a description of some walking on a slippery surface of frozen methane, the danger being a fall in which the spacesuit's hot exhaust might contact the surface and ignite an explosion.

I'd suggest that this is likely to be a somewhat poorly-recalled "The Forever War" by Joe Haldeman.

This does feature "time travel" although this is related to the difference in relative speeds for interplanetary travel due to time-dilation.

"Exactly. You've lost about nine years, though, to time dilation, while we maneuvered between collapsar jumps. In an engineering sense, as we haven't done any important research and development aboard ship.. . that enemy vessel comes from our future!" He paused to let that sink in.

Certainly it features passages where, during training, the possibility of suit heat exhaust causing explosions in contact with a frozen planet/moon surface is mentioned.

"All you have to do is lean up against a boulder of frozen gas; there's lots of it around. The gas will sublime off faster than it can escape from the fins; in escaping, it will push against the surrounding 'ice' and fracture it... and in about one-hundredth of a second, you have the equivalent of a hand grenade going off right below your neck. You'll never feel a thing.

And, finally, I seem to recall one battle where the combatants are forced to take shelter in a force field when a nuclear explosion is caused to eliminate/defend against an overrunning enemy.

I could evacuate everybody to the stasis field, and they would be temporarily safe if one of the nova bombs got through. Safe, but trapped. How long would it take the crater to cool down, if three or four-let alone sixteen-of the bombs made it through? You couldn't live forever in a fighting suit, even though it recycled everything with remorseless efficiency. One week was enough to make you thoroughly miserable. Two weeks, suicidal. Nobody had ever gone three weeks, under field conditions.

There is one I can think of that fits that synopsis, but was written in 2013.

The Synchronicity War by Dietmar Wehr.

It's a series of 4 books and is a good read, in my opinion. In order to effectively combat the opponents, the human race had to quickly invent some adaptive computer intelligence. The constraints on the movement through time are thought out well enough to make the storyline compelling. Both sides progressed rapidly as might be expected when time travel is involved.