I've occasionally had problems with the engines starting and respawning worked.
I'm not entirely sure what you mean by throttle idle, but when I start my engines, I never have them fully closed. Open it the slightest little bit. Too much or too little and it won't start.
That might help
I usually keep the radiators closed to warm up the engine. I start pushing the throttle at around 180-190, opening radiators completely, then off I go. Don't forget full left rudder trim. Good luck!