Three quotes from one page of Thyroid Manager (aspirin is a salicylate):
The most extensively studied compounds that interfere competitively with thyroid hormone binding to the carrier proteins in serum are salicylates, diphenylhydantoin, and heparin.
Some TSH-inhibiting agents listed in Table 5-4, such as, fenclofenac and salicylates, may act solely by increasing the free thyroid hormone level through interference with its binding to serum proteins.
Salicylates. Acetylsalycilic acid has been identified as the most commonly administered medication which may cause significant alterations in measured parameters of thyroid function.224b,224c Salicylate and its noncalorigenic congeners (Fig. 5-3) compete for thyroid hormone-binding sites on serum TTR and TBG.225-228 As a result, the serum concentrations of T4 and T3 decline and their free fractions increase.228 The turnover rate of T4 is accelerated, but degradation rates remain normal.225,226 Salicylate and its noncalorigenic congeners also suppress the thyroidal RAIU but do not retard iodine release from the thyroid gland.312 The impaired respone to TRH313 and the hypermetabolic effect314 of salicylates have been attributed to the increase in the FT4 and FT3 fractions. If this were correct, hormonal release from the serum-binding proteins should produce only a temporary suppression of the thyroidal RAIU and transient hypermetabolism, but both effects are observed during chronic administration of salicylates.225,226 In addition, this mechanism of action does not explain the lack of calorigenic effect of some salicylate congeners despite their ability to also displace thyroid hormone from its serum-binding proteins. In vitro studies have demonstrated an inhibitory effect of salicylate on the outer ring monodeiodination of both T4 and rT3,315 but lack of typical changes in serum iodothyronine levels suggests that this action is less important in vivo. Acetylsalicylic acid mimics some actions of thyroid hormone, but does not reverse classic manifestations of hypothyroidism. While salicylate administration may lower serum cholesterol levels,316 it does not provide a therapeutic effect in myxedema, or lower TSH levels.317 Administration of 8 g aspirin daily raises the BMR to normal in myxedema, accelerates the circulation, and increases sweating, but it has no effect on the skin change, the electrocardiogram, or the mental state.316 Because of some analogies between the effects of salicylates and nitrophenol, uncoupling of oxidative phosphorylation has been suggested as one of its possible mechanisms of action. If this were the case, direct chemical action does not appear to be involved since analogs of salicylate that do not uncouple oxidative phosphorylation in vitro are active in vivo.318
p- Aminosalicylic acid and p- aminobenzoic acid are closely related chemically to salicylate. They inhibit iodide binding in the thyroid gland and are goitrogenic.319,320 These agents also displace thyroid hormone from its serum protein-binding sites.321 Abnormalities of thyroid function tests have been also reported in patients treated with salsalate.322
Numbers refer to references on that page.