I fear if i rely on PCB as heat sink, i "may" damaged my UNO regulator.
The Uno uses a linear voltage regulator to condition the power supplied via the power jack. These devices are rated to deliver a specific output voltage, and up to some maximum amount of output current. However, they need a voltage differential to work. That is, a 5-volt regulator like that on the Uno must be fed more than 5 volts on the input side. This is why the specification for the Uno input voltage is 7 to 12 volts. A 5-volt input will not work.The regulator heats up because it must dissipate an amount power which is calculated by multiplying the voltage differential times the amount of current flowing through it. So with a 12-volt input, the voltage differential is 7 volts, and if the Uno plus the LCD plus whatever else draws, say 100mA, then the regulator must dissipate 0.7W (7V x 0.1A = 0.7W). The regulator on the Uno is a small surface-mount device and there is not a lot of heat sink area, so this much power can get it pretty warm.Alternatives would be a lower voltage input supply (e.g. 9V or 7.5V), or to use an external 5V power supply and bypass the Uno's on-board regulator by feeding the 5V directly in to the Uno's 5V pin. CAUTION on this: Do not exceed 5 volts if using the latter method. A well regulated external supply must be used. I can't comment on whether your 5V 3A wall wart is suitable without examining it. At the very least you should measure its output voltage. If it's a decent quality regulated supply, it may be fine. If it's unregulated, it could well be supplying significantly more than the advertised 5 volts.Hope that helps.
it is exactly 5.2VDC and stays there