Say one takes a healthy 12v battery and drains it to 7 volts.
They then apply a 5 amp charger, one which will actually try and charge such an overdepleted battery
The 7 volt battery is not going to instantly accept the max current, 5 amps. It will instead be extremely resistant to accepting even one amp, and that sub one amp will have the battery voltage likely up in the 14's where is is limited to by the charger.
Over time, that otherwise healthy battery will begin to wake up, and start accepting more and more amperage, and at some point will gladly be sucking up all 5 amps that the charger can make. I've witnessed this take as few as 2 minutes and as long as 15 . Once it wakes up, that 5 amps, or max current of the charging source, will not be able to maintain the battery in the mid 14's, but likely drop down in the low to mid 11's, and rise from there towards the mid 14volt maximum.
An unhealthy, sat on the side of the house battery for a year, at 7 volts, has absolutely no help of ever accepting the 5 amp maximum output of the charger, and ZERO chance of heating it up to levels that would freak out the owner and question the health of their charger.
It will only put out the amperage required to bring the battery to mid 14 volts or so, and that is likely to be a tiny fraction of the chargers maximum 5 amp output.
So the 7 volt battery, maxing out a charger, and thus bringing it to maximum temperature, is simply wrong.
This is provable time and again, if one were to use an Ammeter, and see how much amperage the battery is accepting at a certain electrical pressure (voltage).
Likewise how much voltage a battery can maintain, when providing x amount of amperes, is a fine way of estimating its health and remaining ability. It is called the load test. Variables being how much load applied for how long, and then...compared to what.
A charging source will get its hottest, when providing its maximum current.
It will provide its maximum current when feeding a depleted but otherwise healthy battery, for a long period of time.
A 12v battery depleted below 10.5 volts, well over depleted, as 100% discharged is considered 10.5v on most 12v batteries, needs time, and often a significant amount of time, before it can start accepting the maximum current of a charging source.
I have no idea if the OP's Noco is running too hot, but if it were put onto a known healthy, but otherwise depleted battery, it could be maxxed out at 5 amps output, for quite a while, before it reaches its maximum voltage at which point less amperage is required to maintain that constant voltage.
aAquick search says an H7 battery is 80 amp/hours capacity.
If it were healthy and depleted to 10.5v/ 100% discharged) it would be able to suck up 5 amps for about 14 hours before it would reach 14.5ish volts, at which point the amperes required to maintain 14.5v would taper and it would likely require 2 or 3 more hours being held at 14.5v before amperage tapers to the level the battery can be considered full.
Once they taper to about 0.4 amps @ 14.5v@77f, if an AGM, it would be able to be considered fully charged. Flooded batteries are about double this amount, but it varies with battery age, design, and temperature.
I have tested a Noco genius one on its agm setting, and it had 1 amp available, to bring the battery to about 13.8v, iirc, then 0.5 amps max to attain 14v, and then only 0.25 amps to get to 14.7v, and once it got the battery to 14.7v, it shut off charging current completely until battery voltage fell to 12.69v at which it restarted with only 0.5 amps available.
USE AN AMMETER.
See how much current is flowing at an electrical pressure.
5 amps flowing into A BATTERY at 14.7v means the battery is not close to being fully charged
0.8 amps flowing into the battery @ 14.7v indicates it is.
You can't just see 14.7v and say Yep, that means this.
If a charging source is holding a fully charged healthy battery at float/maintenance voltage, it is likely only using a tiny fraction of its potential amperage output, and even if left on such a battery for a week, will only be a few degrees above ambient temperature.
If the OP's battery is Healthy, and well discharged, then it would suck up 5 amps for quite some time, and the charger would get hot. This would be expected, and totally normal.
Such a charger is obviously not designed to charge healthy, well depleted batteries all day every day, or it would have been designed with better heatsinking and ventilation. Fans and vents to let in dust do not fill the pleasure centers of the modern consumer with joy, So the marketers insist on a sexy package that appears to be waterproof, and the heat producing electronics within simply degrade faster with the increased temperatures.
The following wattmeter can be put inline on the DC output of any charger that does not include a battery temperature sensor on the lead to the clamps, which very few do.
https://www.amazon.com/GT-Power-Analyzer-Consumption-Performance/dp/B00C1BZSYO
It will not only show voltage, and amperage, and calculate wattage, it records the peak/surge wattage, the peak/surge amperage, and the minimum voltage.
It not only displays that, but Also amp hours, and Watt hours. They are not really to be trusted to be accurate below about 0.25 amps, and there are dozens of clones out there.
When one can see how many amps flow into a battery at voltage X, or how much voltage a battery can maintain when powering X amperes of load, then much of the mystery of battery charging disappears.
When one can spin a dial to change desired battery voltage and watch amps respond to the change in pressure, then most all the mystery dissolves.
If Nitro had ever used an ammeter on his charging source, he'd never claim putting his charger on a 7 volt, side of the house battery, would ever be capable of maxing out his charger, as it can't, and it wont, unless perhaps there was a direct short within the battery, and the one shorted cell of the battery would heat as much as the charger would.
The amount of amperage a battery can accept, is very telling of its condition, and a sub 7 volt battery, whether relatively healthy, or sulfated door stop, is not going to accept a lot of amperage.
The healthy but overdepleted/sub 10.5v battery will require some time, before it starts accepting the charging source's maximum output amperage.
Many chargers will not even try and charge a sub 10.5v battery.
A questionable battery whose voltage, measured at battery terminals, that rises quickly with a small output charger, is either close to fully charged, or extremely capacity compromised from sulfation.
A clamp on DC ammeter is also a wonderful tool to have. PLace it next to one wire in a DC circuit, zero the meter, clamp it over one wire, and see how much amperage is passing through that wire.
Multiply amperage times voltage to get the wattage.
