Adrenaline tends to restrict blood flow to extremities, and shuts off cholinergic processes of the body like digestion, saliva excretion ect. Thyroid does not stimulate cholinergic or adrenergic directly, and should promote a healthy quieting and regulation of both sides of the autonomic nervous system. Thyroid should also decrease the temperature difference between the core and the extremities.
However, there are circumstances where increasing the level of T3 in the blood will indirectly increase sympathetic nervous tone. For example, if someone has been in a hypothyroid state for a long time, they can have a chronically elevated level of adrenaline to compensate. And supplementing even extremely small amounts of T3 can suddenly sensitise their cells to the excess adrenaline in their system - and they can have an adrenergic response.