The stock KLR thermostat (160 F) has a decent sized slot to act as an air bleed during filling and to provide some circulation when thermostat is closed. Generally this will allow the air to clear the system but, as Damocles recommended, burping the air from the system needs to be considered.
A bit of sludge can restrict the slot or someone may have installed the thermostat with slot down which leaves more air in the head. I want to repeat what he said that air can be trapped in the cylinder head because over heating of the exhaust valve area can occur to a very high degree despite the temperature gauge reflecting a lower reading.
The radiator fan only comes on when the coolant exiting the radiator exceeds about 210 F which means the thermostat must be open for circulation, and the temperature be above 210 F. The cooling fan's operation confirms that the thermostat has reached temperature and is wide open. In this state air will be forced out of the engine into the radiator and should purge.
If the coolant level is very low, the water pump will not be effective and so not be capable of forcing the coolant lower in the engine to pass through the thermostat bleed hole. This can lead to having the engine almost full of coolant but the water pump unable to build enough pressure to force the air pocket around the thermostat out. In this condition the thermostat would be dependent on heat transfer through the air pocket which often seems not to be sufficient to heat the thermostat. A partially blocked thermostat hole makes this worse because the coolant cannot equalize level.
The pump should fill with coolant added to the radiator because it's a down hill run but some engines can be very difficult. Many modern engines have air bleeds or a prescribed hose removal procedure to burp air. One has not lived until one has burped the air from my 1986 Toyota MR2 for example.
When the water pump is full of coolant and engine rev'd up the pressure against a closed thermostat can reach 60 PSI which shoots coolant through the thermostat hole at a great rate and will purge air almost instantly. If the system can't generate significant pressure, it may not purge the air.
Sometimes people "chicken out" before the thermostat would have opened but I'm often in that camp as can only speculate as to how high the temperature might reach in some pockets.
As Damocles stated, shutting down for a short "rest period" can allow the heat in the head time to even out and to heat the thermostat without over heating some areas.
It's good practice, IME, to measure the amount of coolant drained as a guide to how close to full is the refill. The KLR is not a tough one to clear the air and haven't heard of one damaged by partial refill so wouldn't worry in that regards.