I purchased a Honeywell RTH6300B to replace my current digital T-stat. Everything looked good until I called Honeywell to ask about the heating cycle setting. During the conversation I discovered that this device has a permanent setting of +/- 1 degree F. My current T-stat allows +/- 2 degrees F. This seems like a big difference to me because now when I set my temp to 70, my current stat does not call for heat until the room temp drops to 68. This RTH6300B will call for heat at 69. During the colder months of winter my room temperature drops by 1 degree almost immediately after the reaching my set temperature. If I install this Honeywell, I envision it calling for a new heat cycle even before the fan has shut down from the previous heat cycle. Somehow that can't be good for the equipment. It would be a similar issue with the A/C in the summer "except" the A/C unit has a 5 minute delay to prevent it from turning off and then immediately back on.
Should I return this T-stat and try to find one with a +/- 2 F degree swing? Thanks.

If you will take the time to read your manual that came with your thermostat.You will find that the thermostat is set up on cycle rates. Pick the one for the type of system you have. The cycle rate will not allow the thermostat to do what you are talking about. The good part about this thermostat is that it does have a tight temperature band and that makes it better than 95% of all the other thermostats out there.

Please read Page 20. Function 5 Heat Cycle rate and adjust accordingly.

http://customer.honeywell.com/techlit/pdf/69-0000s/69-1717.pdf

Thanks for your help hvac1000. I already studied the manual and determined that my 92% efficiency gas furnace should be set to 3. But the person at Honeywell was also adamant about the fact that once the room temperature drops 1 degree below the temp setting, the T-stat will call for heat. Otherwise, if the 3 setting only allows 3 heat cycles per hour then you could not keep your home heated to the desired temperature during the winter. Here in Syracuse NY my heat kicks on about every 5 or 10 minutes in January and February to maintain a room temperature within 2 degrees of the setting.
I will agree that I have no clue as to how all this works, if I did, I wouldn't be asking the question.

Install your thermostat and enjoy. It will work just fine. I use Honeywell for all three of my HVAC system zones. Honeywell was also my choice for all my customers and they were happy or I would have been selling something else.

From what you have told me you have

Too much heat loss in your structure
Thermostat located in the wrong area
OR both.

Is there a possibility that the location of the t-stat is such that it sees the rise in temperature quickly.

Thank you for your input. My concern was: when the Tstat reaches its set temperature, the furnace will turn off (as it should). At that time, the room temp begins to deteriorate because there is no longer a heat source. The speed at which the room temperatures declines is the crux of my question. Is the TStat heat cycle of +/- 1 degree is better or worse than +/- 2 degrees. I think that +/- 1 degree will cause my furnace to turn on, off , and back on again repeatedly during the very cold months. I would have the same concern regardless where the Tstat is located.

The tighter the control band the better the thermostat. What we are talking about is accuracy. A one degree accuracy is better than a 2 degree. This is the swing or band of the thermostat. As always tighter is better.

If you like your furnace not to run as ofter by a real cheap thermostat. Then it will drift from set of 70 to 75 then it will not turn on till it gets down to 65.

I think you are driving yourself nuts over something that is not that big of a deal. I prefer accuracy to inaccuracy myself.

If you have a heat register located close to your tstat it will warm up the air near it prematurely causing the tstat to shut down the furnace before the rest of the house is up to temp. As a result the small heated mass of air near the tstat will disipate quickly therefore making the stat call for heat again. My sollution to this was to close all of my upstairs registers except for the ones that are farthest from the tstat such as the ends or perimiter of the house, I just resrict those ones, distance is KEY. This also has a bonus effect of making the basement warmer because having 90% of the registers closed upstairs forces the hot air from the furnace to be expelled downstairs, with the resulting circulating air from downstairs to upstairs making its way to the tstat, by the time it reaches the stat my basement and upstairs are plenty warm. Another effect is by heating the basement more it adds to the overall heat resivoir of the house and naturally increases the time between heat cycles.