Can I hook up a smart thermostat to a "high efficiency gas forced air heater"? Are there any caveats?
It will be perfectly fine. The internal control and safeties of the heater will prevent most bad™ things from happening.
A smart thermostat will come preprogrammed with reasonable defaults for hysteresis and min turn on.
One additional thing you should consider adding is a CO detector, which will alert in case the unit starts emitting the toxic odorless and colorless gas into your living space.