Translation:The engine is heating up.
Warm up is an English idiom. We have no evidence to suggest that Klingons employ it as an idiom too. An engine may be becoming warm, but there is no implication there of becoming ready to use.
Literally, you would say something like QapbeH QuQ the engine is ready to function.
As someone who warms up engines as part of her job, I must say that this is not an idiom. At work I am literally watching the oil temperature gauge, waiting for the needle to reach the green line, indicating a temperature of about cha'vatlh SImyon, considered warm enough for it to be safe to operate the engines at high power. The idiom in English is run up, but of course it would make no sense to say vIqetmoH of engines. QuQmey vIQapbeHmoHmeH vIghunchoHmoHbej. I'm sure there are examples of things that in English are said idiomatically to warm up and it's possible that the engines on the Jetsons' spaceship use a technology that requires preparatory operation for a purpose other than warming, and that the term warm up is for them an anachronistic idiom.
None the less, due to the complicated idioms that are involved, the blurry line separating warm from hot, and the fact that a similar separation of vocabulary exists between the two languages in this case, we will not be accepting "warm" as a translation of tuj in this exercise.
I'm agreeing with most people here:
ghunchoHtaH QuQ - the engine is warming up, becoming warm, which depending on the technology may or may not represent it reaching an optimum operating temperature.
tujchoHtaH QuQ - the engine is heating up, getting hot - time to open the cowl flaps, adjust the rugh/Hap mixture, extend the graphite rods, or whatever you do to protect it from heat damage.
Different concepts, different translations.
(I am honestly not sure if I have spent more time studying Klingon or sitting between engines, but I have strong feelings about both).
Warming up in this context would refer to a machine coming to its normal operating temperature. This sentence is about an engine getting hot, presumably hotter than it normally does.