Your thermostat should have an adjustment that controls the sensitivity of the unit.
Some can be set to 1 degree, so if set to 70 they turn on at 69.
If set at minimum they may need a great amount of difference to act.
Your thermostat may also be bad.
There are many new devices that have clocks and other features to conserve energy, you may want to toss yours and upgrade.
Before you do you will need to confirm the control system of your heater.
Get the make and model of both your heater and thermostat and make a trip the the home store.
Work with the folks there to select a couple different units, they may be able to look up a compatability chart, if not get the manufacturer name and model of the units you like, drop the manufacturer an email containing your information and they will advise if the unit will work and how to connect it.
They aslo can advise if the product is not compatable what might work.
Better to upgrade a $20 item to something that will save its own cost than to wast the energy repairing the old one.