How often should I water tomatoes in 35 degree weather?
Deeply and less often beats a little every day: soak until water reaches 20 to 30 cm, then let the top few centimetres dry. Frequent shallow watering keeps roots near the surface, which is exactly where the heat is worst.
My raised bed dries within a day.
Too much drainage and no mulch. Compost raises water retention, and a few centimetres of mulch on top cuts evaporation by roughly half. Both are cheap; the mulch is the one people skip and the one with the fastest visible effect.
How long does this usually take in practice?
An afternoon to do it properly the first time, then minutes when it recurs. Most of the first afternoon goes into discovering which of the defaults do not match your situation.