How much radiation will I receive with a thallium myocardial perfusion scan?

Depends on dose. It depends on the dose but a rough estimate would be 15 to 20 msv.
10-20 mSv approx. The thallium-201 dose administered varies from one patient to another according to the patient's weight. The radiation from a standard dose varies from 10-20 msv ( milli sievert). In comparison, a flight from los angeles to london gives 0.05 msv and the annual natural background is equivalent to 3 msv. A cardiac catheterization will give 200 msv to the skin.
18 mSv. For comparison, a chest x-ray is 0.02 msv and and abdominal ct scan would be 10 msv. So the thallium scan is like getting almost a thousand one view chest x-rays. These amounts of radiation are not trivial and a certain number of cancers will occur related to the test. If you get multiple tests, the radiation is of course even greater.