Yes, but mainly when the dose is too high. At a correct replacement dose, levothyroxine should not raise your heart rate beyond normal.
Recent evidence
A
2026 systematic review looked at 12 studies with 1,817 patients. It found that tachycardia, palpitations, and atrial fibrillation were mostly not significantly increased at replacement doses. Adverse events occurred mainly when TSH was suppressed. In blinded placebo-controlled trials of euthyroid patients, there were no significant differences. Some symptoms may reflect placebo or nocebo effects. This review is small and pooled studies of varying design, so treat it as reassuring but not definitive.
If you're asking about your own treatment, don't stop or change the dose on your own. Talk to your prescriber and ask for a thyroid function test.