The thermostat bypass hose is part of the updated thermostat housing modification. It is a good thing.
The bypass hose allows the coolant to circulate through the head and cylinder passageways to allow for better heat distribution during warm-up before the thermostat valve opens - reducing the possibility of hotspots developing.
The bypass hose is not the cause of the cooler than optimum running temperature.
Rather, the thermostat itself is the problem. It is the wrong heat range. The OEM thermostat is 180F (82C) for the '98 to '01 TLS, and the '97 TLS may be even cooler.
When the thermostat opens and the ambient temperature is too cool, or the engine is not pushed hard enough, the coolant temp remains below the 176F (80C) threshold point where the ECM switches to the "warm map."
Therefore, a simple change to a hotter thermostat (190F; 87C) will cure the problem and keep the ECM on the warm map. This results in better throttle response and improved fuel economy.
For reference, see page 5-2 in both TLS and TLR service manuals. The TLS manual I have only shows the '97 version, so the bypass hose is missing. However, the TLR manual shows the updated coolant flow path, and it also presents a clearer image.