Temperature of hydronic baseboards

If the water is 180*, the copper should also be 180*.

The copper tube is easy to measure, the fins not so much, it depends on the air current moving through them

Measure the temperature on the copper tube with a strap on thermometer at the very first fin tube run, then at the end of the very last.

Add and divide by 2 to get average water temperature. Those point and shoot temperature guns are not the best on a small diameter copper tube. Some black tape, friction tape, black duct tape, not shiny electrical tape

There is no such thing as an average residential home. Some are designed to run at a boiler temeperautre of 180, which will give you an average real tube temperature (which may or may not be what the IR gun reads —depending on the gun) of around 160 or so — say a bit over 170 at the beginning and 150 at the end. But maybe the system was plumbed in series, so one room might be at that temperature, but another — four baseboards down the line — at only 130. Then other systems may be designed to run at a much lower temperature — perhaps as low as an average of 130 or 140. Other systems, with outdoor reset, will vary from day to day.

It's the same kind of question as "how big is a box?".

The surface temperature depends on what surface you are talking about. The surface of the copper pipe that is feeding the first radiator will be close to 180°. Maybe a few degrees cooler if the pipe from the boiler to the radiator is in a cold crawlspace. On the last section of baseboard, the copper temperature will have dropped as much as 40° or more depending on the amount of element and the room temperature. In a perfect world, the room air temperature entering the bottom of the radiator will be exactly 65° and the amount of element will cause the last section of radiator to be 20° cooler down to 160°. That would make the 4 GPM flow thru that loop of baseboard deliver 40,000 BTUh to the room.

If you are talking about the sheet metal cover of the radiator, then that temperature is substantially less. That temperature will depend on the temperature of the entering air at the bottom of the baseboard assembly. It will certainly be lower than 160°, but how much lower is only a guess. I might hazard this guess to be about 140° from personal experience. I remember holding a cover with gloves to remove it for cleaning so that would have made the cover over 120°.  I know that I can keep my hand on a 120° pipe, and I can not hold on to a 125° pipe so I often used the touch test to determine temperatures.

I hope this info helps