Good answer. There could be considerable voltage drop from battery to tv. The tv has a watts rating, not amps. The lower the voltage at the tv inputs, the greater the current. You may be exceeding 7.5A.
You can measure the voltage drop between battery & tv. Put one voltmeter probe on the + battery terminal and connect the other probe to the + tv input. The meter should be on the 2V scale. The meter leads will need to be lengthened for this measurement. Measure the ground cable the same way.
You can also measure the tv current. Voltmeters usually have 10A capability. Remove fuse and insert amp meter.
Now we got all the pieces of the puzzle to fix it right!
westend wrote:
Amperage increases with lowered voltage. If you have small wires connecting the TV to the DC source, you will have voltage drop and increase the amperage and the heat. The same is true for a partially discharged battery when powering DC devices.