Factory oxygen sensors were the one-wire, non-heated variety. Back in the mid 80's the emission standard wasn't as stringent, so the O2 sensor operation wasn't that critical.
There are advantages to heated sensors; mainly, getting the engine into closed loop sooner than the unheated version. This means your ECM will respond properly in less time than the original setup. Also, the heated sensors are less prone to fouling, especially when using a lead mix or additives.
Oxygen sensors must be hot to properly monitor oxygen in the exhaust stream, somewhere around 800-900 deg. F. The heat generated by the exhaust is what gets them going, and the backpressure in the system keeps the temperature up to spec. If the exhaust system scavenges too quickly, the sensor will not reach its normal operating temperature, especially during deceleration, so the exhaust stream runs the sensor too cold. Running a heater at the sensor element keeps it at its operating temperature.
When you modify the TR exhaust by making it freer-flowing, the stock one-wire sensors no longer work reliably, forcing an incorrect reading and low cross counts - thus making your engine run too rich. The heated sensor overcomes this dilemma, keeping the sensor signal fully active and maintaining proper cross-counts.
For what it's worth, OEM's have used heated sensors exclusively since around 1996.