An apparatus T.sub.1 for sealing a well tubing 12 including a housing 20, 21, 22 which has a channel 68 communicating with the bore of tubing 12 and a chamber 43 connected with channel 68. A seal 62 is slidably mounted in the housing and is disposed in a retracted open condition in chamber 43 to enable fluid flow through channel 68. AN actuator 41, 42 also disposed in chamber 43, includes a shape memory alloy material which is responsive to the temperature thereof rising to a predetermined level corresponding to the transition temperature of the shape memory alloy for transforming in shape to extend the seal into an extended condition within channel 68, thereby blocking fluid flow therethrough.