Traning for 2x250km in 4,5 months Is this possible? The goal is to do this in 3 days - ride 250km one day, then take one day off, and ride 250km again the next day, all on a road bike, with about 2500m of total elevation gain, in 30C temperature, on a rented road bike (not saving money here).

Maximum distance I've done the last season was 200km on a trekking bike in one day, and that was after 1-2 months of training. 100km was my record on a road bike.

There's winter in my country, so I'll be able to ride hopefully in March, which means 2-3 months in a gym/running/swimming, and then just about 2 months of actual riding.
You don't say how young and foolish you are.  Many years ago, at age 17, I rode a double century (a little over 300 km) with about that much climbing with no training at all.  I had never ridden more than 50 km in a day.  The weather was much cooler than 30C.  The hard part about the second trip would have been psychological-I found the double to be much more than was fun.  I rode a number of centuries, 160 km, afterward and found them fun, but the double took 16 hours.  I was on a decent 1960's road bike. If you have done 200 km already, you have a good idea what it takes.  You can get a lot stronger in 2-3 months of training.  Go for it.