I don't think it's any indication whatsoever of possible heart problems. Although thyroid meds are a synthetic hormone, they're just like any other drug and have side effects, one of which is a faster HR. You also might find that this goes away as you recover more from your surgery...it takes longer than you might think. Also, you're probably not yet at your "ideal" dose of Synthroid. Sometimes this takes some fine-tuning.
Does this mean I will have heart problems?
Synthroid does increase HR, in some people more than others. It does this by increasing the adrenalin receptors in the heart. Some people find switching to a different brand name or from generic to brand helps.