Service manual suggests feeling the inlet and outlet hoses of the coolant bypass valve (below the accumulator, #6 in the attached picture) after the engine has gotten up to temperature with the rear heat set at its warmest setting. If there is a noticeable difference in temperature between the two hoses, there is probably an issue with the valve or its controls.
There is also a service bulletin for poor rear heat performance on 03-05 extended Trailvoys: #05-01-37-002A. Here's the brief description:
Condition
Some customers may comment on poor 2nd and/or 3rd row seating heater performance when the vehicle is at idle.
Cause
This condition may be due to lack of coolant circulation to the rear heater core.
Correction
Install auxiliary heater pump package, P/N 89024885 (L6 Engine RPO LL8) or P/N 89024886 (V8 Engine RPO LM4 or LH6). This pump will improve coolant flow to the rear heater core.
There is also a service bulletin for poor rear heat performance on 03-05 extended Trailvoys: #05-01-37-002A. Here's the brief description:
Condition
Some customers may comment on poor 2nd and/or 3rd row seating heater performance when the vehicle is at idle.
Cause
This condition may be due to lack of coolant circulation to the rear heater core.
Correction
Install auxiliary heater pump package, P/N 89024885 (L6 Engine RPO LL8) or P/N 89024886 (V8 Engine RPO LM4 or LH6). This pump will improve coolant flow to the rear heater core.
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