I don't think the Battery temp sensor is used at all for intake heaters, however I recall the engine coolant temp sensor is also used for high idle functions and 3 cyl idle functions. Maybe it is used as well for the intake heaters? Is your coolant temp sensor working?
This is from the service manual:
OPERATION
The Engine Control Module (ECM) operates the 2 heating elements through the 2 intake manifold air heater relays. Refer to Powertrain Diagnostic Procedures for an electrical operation and complete description of the
intake heaters, including pre-heat and post-heat cycles.
INTAKE AIR TEMPERATURE SENSOR
OPERATION - DIESEL
The IAT provides an input voltage to the Engine Control Module (ECM) indicating intake manifold air temperature. The input is used along with inputs
from other sensors for intake air heater element operation, for engine protection, fuel timing and fuel control. As the temperature of the air-fuel stream in the manifold varies, the sensor resistance changes. This results in a different input voltage to the ECM.
BATTERY TEMPERATURE SENSOR
OPERATION
The BTS is used to determine the battery temperature and control battery charging rate. This temperature data, along with data from monitored line
voltage, is used by the PCM to vary the battery charging rate. System voltage will be higher at colder temperatures and is gradually reduced at warmer temperatures.
The PCM sends 5 volts to the sensor and is grounded through the sensor return line. As temperature increases, resistance in the sensor decreases
and the detection voltage at the PCM increases.
The BTS is also used for OBD II diagnostics. Certain faults and OBD II monitors are either enabled or disabled, depending upon BTS input (for example, disable purge and enable Leak Detection Pump (LDP) and O2 sensor heater tests). Most OBD II monitors are disabled below 20°F.