It might not have the production values that Codemasters are able to achieve but Classic Racers still looks like a reasonably good hill-climb racer and it's now on Linux.
Linux support arrived with the 1.2 update released a few days ago. With that, it also introduces an early implementation for supporting steering-wheels, rumble support, graphics and UI upgrades, an unlocked frame rate (it was locked to 60FPS before) and so on.
The game offers 4 different car categories from "micro cars to F1", 11 unique tracks and 6 championships to race in. Considering it costs less than five pounds though, don't go expecting too much from it.
The trailer doesn't exactly have the best quality and the in-race UI looks pretty terrible, but the saving grace seems is the driving which actually looks quite good. For a cheap, casual racer it might be fun for a while.
You can find Classic Racers on Steam.