Not sure if its known exactly why, but there are several suggested reasons, possibly acting in concert to produced increased or decreased TPR in hypo and hyperthryoidism respectively.
Two possible mechanisms I've come across are 1) increased heat production in hyperthyroidism leading to vasodilation, and 2) direct effect of T3 on vascular smooth muscle.
"To exert its cellular activity, T4 is converted to T3 via the enzymatic action of iodothyronine deiodinase. The two types of iodothyronine deiodinase, type I (DI) and II (DII), are expressed in different tissues. DI has been found in the thyroid gland, liver, kidneys and other tissues and DII in a limited number of tissues, such as the CNS, anterior pituitary tissue, human skeletal muscle and brown fat in the rat.[14,15] DI activity is known to be decreased in the hypothyroid state and may play a primary role in regulating circulating T3 levels, while DII activity is increased in hypothyroidism and probably regulates intracellular T3 concentrations.
3,5,3'-triiodothyronine represents the metabolically active thyroid agent that possibly has a vasodilatory effect on the vascular muscle cells. Hypothyroidism and T3 deficiency are associated with peripheral vasoconstriction. DII was identified in cultured human coronary and aortic arterial smooth muscle cells. DII is believed to be responsible for the local conversion of T4 to T3 in these vessels. It has been demonstrated that the expression of DII in vascular smooth muscle cells is dependent on a cAMP-mediated mechanism. T3 inhibits DII activity at the pretranslational level (inhibition of DII mRNA expression). DII expression has been reported to be increased in hypothyroidism and to have a protective action on human vessels. Local production of T3 by DII is another vasolidating mechanism mediated by cAMP. In normal thyroid function there is a balance between these vasoconstrictor and vasodilator mechanisms."