Not if the disease is stable. Hashimoto's thyroiditis usually "burns out" and you become hypothyroid at some time. You need to submit all pertinent medical records; current status to include names and dosage of
medication(s) and side effects and current thyroid function tests to your AME. If you are "euthyroid" (the TSH is normal) the AME can issue the medical and forward the records to the FAA. If the TSH is not normal, it will require a decision by the FAA.
Again, this is a condition that requires FAA approval to fly. You should self-ground and either take the information to your AME who can talk to the FAA or mail the information to the FAA and wait for their approval to fly.