The answer is different for different types of heaters.
Any heater that has a lamp inside that gets bright, will reach maximum heat in a fraction of a second. This is due to the short-wave infrared technology used in these types of heaters that give an instantaneous heat.
Any heater that uses a carbon lamp, which is normally longer and has a coiled wire running through the middle, can take between two and three seconds to reach its maximum heat.
The only heaters that perhaps need to be considered are the long wave heaters. A long wave heater is one that does not contain a lamp and does not give out any light. These heaters can take two or three minutes to reach maximum heat.