I am wiring 3 baseboard heaters 2 1500w in series attached to one thermostat and 1 1500w heater on the other thermostat. I was planning on having them all on the same 30amp circuit but the thermostats (digital programmable) are rated for 16.x amps. Is it OK to have the thermostats on a 30amp circuit? They would not have 30amps going across normally them but if something went bad I suppose they could.

That is fine. The thermostats need to be rated for what they are controlling.
The 3000 watt load is only 12.5A.

Just seems like if a heater went bad and started drawing a much larger current the thermostat would not be able to handle the current draw and the breaker would not trip.

How can a heater go bad and draw more current?

Not sure how it would since its already getting its heat from resistance. Speaking more hypothetical. Appreciate your help...

Well, if there is a problem like an element shorting out the fault current will definitely trip the breaker.
Nothing can really cause the heater to draw more than it's rating for very long of a time.