Hi,
Since you say that this is an Li-ion battery that brings in a set of special considerations. There is a lot written on the web about this so you could do more reading too. I will mention the main points that every system designer should know and take into consideration.
1. One is the terminal voltage, which must be controlled precisely, and you already know about that one, which is good.
2. The second is current limiting, which must be found from the data sheet.
3. The third is the low current cutout point, which many 'believe' is a safety factor because of possibly plating of the electrodes which destroys the battery over time, shortening it's life.
4. The fourth is a timer to make sure there is no way the battery can be charged indefinitely.
5. Charge balancing.
6. Temperature sensing (optional).
[1] For #1, we want a circuit that can detect the voltage and either turn off the charge current or reduce it in order to keep the voltage from going too high. There are two basic approaches: Abrupt and gradual.
With a purely linear charger, the current is cut back little by little so the voltage never gets too high, and then when the current gets to a certain low level like 5 percent of normal charge current, the charging is shut off completely and never allowed to turn back on without user intervention, or alternately until some low level voltage has been reached (like 3.5 volts).
The above is considered a very good method.
If the voltage is to be simply cut off though, then we need to think about having a pretty accurate set point and turn off the charge controller and not allow it to come back on until the battery has reached some low level again like 3.5v. If this happens too fast though, the timer would prevent charging anyway, and thus prevent a faulty cell from being constantly charged.
[2] Current limiting is not too difficult, the current has to be monitored and the controller forced to cut back the current level if it goes too high. If the source can never supply the normal charge current however then it may already be current limited. If the panel can not supply say 1 amp when the normal charge current is 1 amp, then we might consider that already limited.
[3] As the battery gets close to full charge, the current can get low, and very low current is not considered good for an Li-ion because it is not enough to reach the point where the charge acceptance is high enough to actually charge the battery. Instead it causes plating, which ruins the battery. So some low level cutout is also a good idea. I think the consensus here is that 5 percent of the normal charge rate is the right cutout point. So if normal charging is 1 amp then the low level cutout is 50ma. Anything less than that might be considered too low. Personally i think it can be lower, like 25ma, but i dont want to interject any personal views too strongly here. The way i charge my cells is i never leave them too long anyway, but that requires human intervention something that a completely automatic system doesnt have.
[4] The timer is the last safeguard. This prevents charging for too long if something else goes wrong, which might include a significantly aged cell since it may never get to the fully charged state.
If you charger design takes into account all four (1 through 4) of these things, you 'll have a very good system which would be safe. You can add temperature sensing to that, but that's not always done. Temperature sensing would be done in an environment where it would be extremely hazardous to have something get too warm, or if you want an extra built in measure of safety.
[5] If your battery includes multiple cells in series, then you have to also think about charge balancing. Since they dont make a 14.4v cell, there must be some cells in series for this pack. That means they probably have a built in charge balance mechanism but you could check that. It could be made from circuits that are internal to the pack that bypass certain cells that are considered charged already.
Now a quick note about the methods i have used in the past with great success.
Linear or pseudo linear charging with gradual current cutback, with second isolated circuit to monitor charging. This includes secondary voltage and current measurements to detect any fault of the primary charge system.
I've also used a purely linear circuit with gradual current cutback, using a simple LM317 circuit which i can post here if needed. A few parts does the trick, but we'd add low level current cutoff.
BTW, the battery never 'uses' all the current. The current flows through the battery, but the current can still be measured using one of many types of circuits to measure current just like a multimeter would do. So the current does not get 'used up' or anything like that.