Turbojimmy has a great point- you get a voltage drop across the thermostat when the contacts are oxidized. When you first turn the thermostat up for heat, there is more pressure on the contacts -> less voltage drop. You also typically get a voltage drop across the sail switch (a.k.a. air prover) and high limit switch.
The board will usually work down to around 10.5 volts, but it's nothing to loose 3 volts across those items.
If you have the original thermostat, I would change it, no question. Cheap, easy, and really needs to be done.
That said, I still recommend an inspection and cleaning.