Final answer:
Type TW cable, with a typical maximum operating temperature of 60°C, should not be used in environments reaching 65°C as it could jeopardize safety. Doubling a wire's resistance by temperature increase is a theoretical scenario unlikely to occur under normal household conditions.
Step-by-step explanation:
The question of whether Type TW cable can be used in an area with an ambient temperature of 65°C addresses the issue of thermal ratings of electrical wiring. Type TW is a designation for a specific type of thermoplastic-insulated wire. The 'TW' stands for 'Thermoplastic Wet' indicating its suitability for use in certain conditions. However, Type TW insulation is typically rated for a maximum operating temperature of around 60°C. Thus, using it in an environment with an ambient temperature of 65°C would exceed it's recommended limitations and is generally considered unsafe.
Regarding the part of the question that involves a change in resistance, for a wire, originally at 20.0°C, to double its resistance, it would depend on the material of the conductor and its temperature coefficient of resistance. This increase in resistance due to temperature pertains to the physics concept of electrical resistance increasing with temperature. Under ordinary circumstances in household wiring, this scenario is unlikely as the ambient temperatures don't typically reach high enough levels to cause such a drastic change in resistance.