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Depending on your part supplier, the LM7805 can have a Theta of 19 or 65 C/W. That is a huge difference. So I reran the calculations. At 200mA with Theta = 19 C/W you will hit about 60C max. I also ran the calculations at 500mA and put them in an attached image to show others how to do them. It looks like if you have a TI part you will probably be OK but still running really hot. I'm still concerned that since there is no air flow over the package it will heat up past the melting point of the plastic. Keep plugging away!
That setup will get over 125C if you draw about 200mA. 7805 has a theta of around 65C rise per watt dissipated. You will have 7-9V drop (14V to 5V). The voltage drop times the current is the power dissipated in the regulator. That power times the theta value is the temperature rise of the part. The plastic used in that adapter is probably only hard to about 100C. At 200mA this will melt the plastic and probably short the whole circuit out in the lighter socket. Please be careful with this and monitor it closely.
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