What would happen if the level of thyroxine in the blood stream could not be detected by the hypothalamus?

The person might probably die.

The principal function of thyroxine is to stimulate the consumption of oxygen and thus the metabolism of all cells and tissues.

Thyroxine is termed T4. It travels through the blood to the target cells and becomes converted to triiodothyronine or T3.

T3 is the active form of thyroxine. T3 enters the target cell's nucleus binding to genes responsible or involved in the metabolism of sugar in the body. T3 stimulates these genes and in so doing metabolism (conversion of oxygen and calories to energy) is carried out by the cell, which also results in generation of body heat.