Minutes, not hours. Infrared heaters warm people and surfaces directly, so the congregation feels the benefit almost as soon as the system switches on. A typical church can turn on five minutes before the congregation arrives and off the moment they leave.
Compare that with a gas convection system, which has to heat the entire air volume of the building before anyone feels warm. In a large nave with a high vaulted ceiling, that can mean firing up the boiler two or three hours ahead of a service, and most of the heat rises straight past the congregation to sit uselessly at the ridge.
The difference is physics, not marketing. Convection works by warming air; infrared works by warming objects. Air is a poor carrier of heat in a draughty building with gaps around every door and window. Surfaces, pews and people absorb infrared energy directly and retain it.
For a church used once or twice a week, this fast response time is where the real savings sit. You are not paying to keep a cold stone building warm between services. You are paying for the hour the building is occupied, and nothing more.