Our 2008 RX400h gas engine (ICE) is on most of the time, thats normal. It always comes on within 15-30 seconds of starting it when cold. Typically, the only times the ICE shuts down is when coasting or at a stop. Sometimes you can drive it slowly in a parking lot (or stop-and-go traffic) on electric only, if it's warmed up (that means oil, not coolant). It's not an electric car, it's a hybrid.
The RX400h does a respectable 24 mpg average, that's pretty good for a 4300# SUV. My old Jeep Grand Cherokee got 12 mpg, my little BMW 330Ci get's 18 mpg (all around town, it can get 23 mpg highway). Our Prius gets 50 mpg.