although you can use a 12V and 3A supply, I think it might not be a long term solution. The power supply will get a little hot since it’ll have to operate on a higher current values. Anyways, do let us know what you found out after using this adapter. The adapter probably will be okay since it has a higher rating than required. Looking forward to your experience since it’ll add on to our existing small pool of knowledge.
If your voltage regulator IC is getting heated up that indicates that it is being forced to supply a lot of current. Now the current being supplied by the voltage regulator IC might not be more that the absolute maximum as written in its datasheet but it still does get warm if proper heat sink is not provided for high current applications. A usage of high current by your circuit can indicate a lot of things as well such as faulty IC or something similar.