The cost of a low end thermostat is approximately $25. Programmable thermostats are estimated to save up to 7% per month in utility costs.
Let's look at some numbers. First of all, we'll be generous and for the sake of round numbers, let's say your gas bill averages $100 in the winter. In just 3 months of winter, you will practically have the cost of the thermostat paid in full.
If your gas bill is $300 a month, the programmable thermostat will pay for itself in just a little over one month. The other 2 months of winter you will save the $21. Not to mention the savings in the fall and spring, when the days are cold enough to run your furnace.
They are really easy to program. Even most of the cheaper models have 4 different programming levels per day, and 2 cycles per week. One cycle for weekdays and one programming cycle for weekends.
As far as replacing the thermostat, there are directions in the box and they are easier to replace than setting up your average entertainment center or home computer system.