Trouble on the Tempus is a game about travelling through the depths of space in a lovely spaceship … as it catches fire and the electronics explode and it falls apart around you. You're pretty much doomed. Luckily you're in a time machine, part of an exploratory mission to test the latest time traversing technology, but you pushed the ship too far and things have gone horribly wrong.
Fortunately, as mentioned, the Tempus is a time machine. Your science officers have jury-rigged it to perform very localised jumps of the crew, allowing you to transport yourselves back to a time when you were not about to explode hoping that if you can gather enough information about the future you may be able to prevent the your ultimate destruction.
Of course it's not a perfect system, if you cause too many paradoxes the ship may find itself trapped in a fate much worse than exploding in the depth of space, if such a thing is possible.
Trouble on the Tempus is a co-operative game of disaster management where the players must prevent fires, electrical faults, and mechanical failures, as they work to fix the hyperdrive of the Tempus so they can power themselves home. Tragically this is a truly impossible task so the players will have no choice but to engage the ships time drive, resetting the board to the way it was at the start of the game so the players can try again with the added knowledge of when and where the disasters will appear.
If you can repeat the timeline enough, collecting the right equipment and positioning yourselves to pre-empt the disasters as they happen, you should be able to predict enough rounds to fix the hyper-drive and win the game. However, each time you time travel you cause a paradox, and the difficulty of the game can be adjusted by how many paradox's you can cause before reality collapses in on itself.
—description from the designer