How can the control unit relearn what the air temperature is? It can't, it relies on the very sensor that has been modified to tell it what the temperature of the air in the air box is. Therefore, if your bike is improved with the addition of an accelerator module it will remain improved indefinitely, until you take it off.
Actually, this is entirely possible.
Most ECUs have "learning" maps to account for sensors drifting out of spec. The lambda sensor is constantly gathering data which the ECU will compare this to it's various map tables and if it senses a different AFR (Air Fuel Ratio) from the one it expects to see it will log that and use it to correct for the appropriate sensor - typically it will correct at least the MAF (Mass Air Flow meter) and make ignition timing compensations.
This is because since air density differs with air temperature, the ECU will expect a higher mass of oxygen when the ambient temperature is lower. Since the ECU is being tricked into thinking the air temperature is lower than it really is, it will inject more fuel or alter the ignition timing to maintain the target AFR. Since this extra fuel or altered ignition timing is not actually required, the volume of O2 in the exhaust gasses will not be what the ECU expects to see. It will therefore think that it is getting duff readings and learn this discrepancy in order to compensate for it in the future. The "learning" is likely to be more significant in newer ECUs than older ones and certainly more significant for drive-by-wire throttles.
As an aside, the guys making these devices claim that they work when the ECU is in Open Loop fuelling mode and cause it to enrich the fuel mixture. This is only part of the story. What these devices do is trick the ECU in to using the wrong value from
Air Temperature vs Fuel Enrichment tables and
Air Temperature vs Ignition Timing Adjustment tables. The latter of these two tables is probably the more significant IMHO even though it is not mentioned in the technical info on the manufacturers site (which just goes to show that, worryingly, manufacturers sometimes only have a rudimentary understanding of engine management systems). Anyway, neither of these tables are usually specific to open or closed loop fuelling - they are simply "adders" that are used to calculate final fuelling and ignition timing values and are therefore used in both fuelling modes.
In fact, the improvement at low RPMs mentioned by many people and touted as one of the main benefits of these devices by the manufacturers means that it is very unlikely that they only affect open loop fuelling. Why? Because ECUs tend to stay in closed loop fuelling except at higher engine loads (i.e. wide throttle openings) since closed loop fuelling is more accurate and better for emissions. The reason for switching to open loop fuelling is that at higher engine loads most lambda sensors go out of range (typically, they are only accurate within a very narrow band e.g. lambda +/- 0.1 or in other words 0.9 to 1.1 * stoich) and therefore the ECU can't rely on them at that point. Instead, once outside this range, the ECUs use look up tables for injector duty cycle, ignition timing, air flow, etc to try and hit the target AFRs for a given engine load.
That's not to say these devices don't work or that they will cause damage to the engine - in fact, I'm pretty sure they work and are also unlikely to cause harm especially as the richer the mixture and the more ignition retardation there is, the less detonation you're likely to see (perhaps be a little coking but fuel enrichment is unlikely to be that high). It's just the device manufacturers theory behind how they work isn't quite right.
): Smoother, seemed to have better drive in all gears, nice added umph in 6th.
