Can this be used with an extension cord?

The thermostatic disc does need to be where the pipe temperature will reflect the temperature of the pipe to be protected. However if you check the manufacturers web site www.easyheat.com you will see the main problem is " Heating cables MUST be installed in compliance with ALL National, State and Local codes." and they advise you contact your local electrical inspector for details on same. As I recall electrical codes go so far as to give the distance said outlet can be from the tapes location. The manufacturer also advises one to use a ground fault protection device (GFPD) and Easy Heat makes one suitable for outdoor applications, these should be available at the Lowes store where you got the tape. This is to reduce the danger of fire from a damaged or improperly installed device, as the electrical fault currents caused by same may not be large enough to trip a conventional circuit breaker. If the Electrical Pro at your local store is a licensed Electrician they might be able to answer some of your questions or know what local offices you might contact.