You are correct that having a hot radiator on what's effectively a cold space - the porch - is very inefficient and, presuming nobody's on the porch most of the time, wastes a lot of energy.
And you are correct that the hot water going into that radiator is being cooled in the process.
However, it is unlikely that the water is going to any other radiators, but rather it's going back to the boiler to be reheated. Nevertheless, you are right that stopping water flow to this radiator will save you on your heating bills.
But - if you stop the flow of water through the radiator, no amount of insulation will keep the pipe from freezing, because with no place for the cold water to go, the hot water in the rest of the system WILL NEVER reach the pipe you insulated. It's just like turning on the hot water in a cold bathroom - the water runs cold for a while even though the hot water is available elsewhere in the house.
On a cold enough day, the stopped pipe with water in it will freeze, no matter how hot the rest of the system.
The best solution to this is to remove the radiator completely. To accomplish this, you need to trace both the input and output pipes for the radiator in question back to an interior space that doesn't ever drop below freezing. The entire system will then need to be drained, and the input and output pipes cut off and capped so that the useless radiator can be removed.
EDIT:
Since you're looking for a short-term, this winter solution, here's what you can do for now to minimize the waste.
- DO NOT TURN OFF THE RADIATOR
- DO turn down the radiator to as low as you can get it without shutting it off. You don't want it to have a chance of freezing.
- Wrap the radiator in blankets to keep in the heat it does generate and conserve energy as much as possible.
Do you know for sure that this is a hot water system? Sometimes steam can sound like running water. If it is hot water, there is a giant air bubble in the radiator preventing it from filling. It needs to be bled off by opening the small valve near the top at one end. You will typically need some sort of tool or key for this. Slowly open the valve. Along with the air, hot water will spit out, so be careful. When there's only water coming out you're done.
If it is a steam system, there is an automatic air vent valve on one side or the other about half way up, it looks vaguely like a small bell. It's clogged up for some reason, preventing air from being vented, meaning steam cannot enter the radiator. It either needs to be unclogged or replaced.
Best Answer
I can't say I'm familiar with your setup, but only with big old radiators & baseboards of the same principal & setup. Your problem is no problem in those systems, they are just to circulate water in one direction of a daisy-chain. The only definition of inlet was which side a flow management valve was installed on.
But, definitely get the plumber back out to inspect his work with you & explain how the system works. In your case I would assume it also doesn't matter at all because your system is actually zoned (it better be), meaning that this radiator might be its own loop & in is out & out is in regardless of what end & what pipe is where.
Don't prejudge & stay calm, just ask him back out to briefly explain the system. You'll need him friendly when the system goes active to adjust the zones for your maximum comfort & overall house balance.
Due to your response indicating this is indeed the start of a zone, the best fix would be to just swap the pipes at the manifold in the basement (or wherever) as the other radiators after the incorrectly installed unit are just flow-through units. Proven by their working perfectly with the first unit being essentially bypassed almost entirely.
No cause for panic nor messy permanent repairs, like replacing the entire zone. The plumber may have initially intended the incorrect unit to be a flow-through, but had to change his plan if a zone was added after the fact (& he/she forgot about the reversed plumbing). I don't know the entire situation, I'm just explaining & not excusing, a proper repair is absolutely necessary.