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This is the part that's causing the problem. You can temporarily disconnect the electrical connector to the TCC solenoid until you can get it repaired.
It's simply the nature of the failure, it gets hot and the solenoid sticks.
You can leave it disconnected indefinitely if you wish. The concern is gas mileage will suffer and the trans will run slightly hotter. Heat is considered enemy no. 1 for transmissions. There is no way to predict how long is okay, some people have no trouble leaving it unhooked. The professional approach is to replace the TCC, so there will never be data collected to determine a time period. I wouldn't worry about it personally, but must warn you of possible consequences.
The cost depends on the labor rate in your area. Costs $150-175 here, might approach $300 in some areas. Many places flat rate. This means you can call (have your VIN no. handy) and they will quote you the actual cost before repair.
You have not accepted my answer and I need to know why? I answered your initial question. Then I answered three follow up questions. Please tell me what I need to do to improve my answers, I live in shame that I could not satisfy you.