If none of these materials is available to you you can always elect emergency service to soak rags or towels in hot water and wrap them around the frozen pipe. This will probably take longer than any of the methods previously mentioned.
After you have checked these areas, take a close look around the refrigerator, both inside and outside. Is there any usual condensation that could indicate a water leak somewhere? Is the icemaker hose fastened securely to the water line repair line? Check also for any water spots on the floor, as these are typically clear signs of a water leak somewhere.
A c clamp or hose clamp is use full for securing or holding the rubber used to seal leaks on piping. However, a clamp should be used carefully considering the type of pipe being repaired, clamping too tight will fracture the pie leaving you with a bigger problem than you started off with.
Service magic only let's licensed and insured tradesmen advertise on the site so that would be a great place to start. I would recommend getting at least three different quotes from different companies. This way you have an exact price of how much your works are going to cost and you will know exactly what you are getting for your money. You will also get the very best price for that work. Most plumbers will often try and sell you work that maybe you don't need as they are trying to make a living.
Plumbers, like all other companies, are required to be on time and act professional. If they have called before hand to notify you then, this can be overlooked. However, if they turn up without apologising for being late, then they may not be the right plumber for you. Remember first water line repair impressions are everything. If they lack a good first impression then this may indicate that it is going to have an impression on their work. In most cases, you would have taken the time off work for the plumber, and what can be worse than waiting all day waiting for them to arrive?
For a newly installed icemaker, you will need up to 24 hours to let the machine function and cool down. A newly installed icemaker may not work until the ice mold temperature has dropped to about 15F - 16F degrees. If you have just added a water line to the refrigerator, it may take up to about an hour and a half for the machine to start working. Also, a newly installed water line may have air in the line. It can sometimes take a few ice making cycles to clear the line of air.
A large plumbing job, such as re-piping or installing additional fixtures, may require a permit. Check with your city's department of building and safety before asking for estimates, and avoid any plumbers who are reluctant to comply with regulations.