frozen pipe part 2

I broke the ceiling in the garage and I found out why the pipe froze.
first of all it was quite cold last night, second of all the pipes for the kitchen pass very close to the garage wall through the ceiling/floor of the kitchen, along the drain. for some reason a very cold current of air is coming out of this hole where the pipes are entering
I unfroze the pipe with a hairdrier (it din't take long) and now the water flows and the pipe is very hot.
#1 no water is dripping out of the wall and I don't hear any noise. I assume that if the pipe was cracked it would be like a volcano under he wall, since the water has high pressure and so on. so therefore the pipe didn't crack?
#2 the pipe goes to the top floor kitchen too, except in that appartment there's no kitchen cause we're remodeling. so I can't let the water drip. tonight it will be very cold again so I will let the water drip in the bottom floor kitchen but I can't do it in the top floor. if the water is really hot in the bottom kitchen end of the pipe, can the water in the same line still freeze in the top kitchen, some 8 feet above? this is for the hot water line what about the cold water line? it will drip too in the bottom kitchen, but it will be cold, not like the other pipe.
eventually the pipes will be relocated a few inches away from the garage wall, along the garage ceiling, and they'll be insulated, but for tonight, and probably the rest of the winter they'll stay in the same place. is there anything I can do to prevent them from freezing again and cracking?
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j j wrote:

in the wall and it keeps the pipes warm.. so they dont freeze.....
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Light bulb(s) and an extension cord near the area where you are having the problem.
John

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I am in the middle of going through something similar this week (long, boring story). What I have done on a temporary basis is install two "stop-and-waste" cut-off valves at the lowest point in the lines going to the problem area above (within a back exterior wall). Then I shut off the water to those lines and drained them out until the repairs and remodeling can be completed. If your upstairs bathroom is not is use, you might be able to isolate and drain those water lines for now.
Also, opening air access into those parts of the wall where the pipes are located and allowing house heat to enter that area might help for now.

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