Newly installed honeywell RTH230B thermostat; when the heat clicks on the fan runs for about 10 seconds, stops for a bit and then restarts and heats the house. This did not happen with the old thermostat.

Rth230b is a digital stat is +/- 1 degree accurate
But u also have u check what's is the status of flame icon.
If fan stops and flame icon disappears that's means its satisfing the set point
But if flame is constant then there is some problem