When we try to increase the heat temperature, the furnace will turn on (the burner will ignite & blower kicks in) and all of a sudden the it will turn off. It repeats the process about 2-3 times. A light indicators in the furnace is red light -slow and green light - fast blinking. Few hours later the furnace will go on and it continuously go on. Then the house will be heated. It seems that when I want to increase the temperature, it will not work.
How do you test if the thermostat (we have an electronic one) is bad. Or how do I know idf there is something wrong with furnace.
I hope someone can help us. Thanks.

Is the furnace itself electric or gas?

We have gas.

Check the pilot light ours does the same thing when it goes out. If not then I would guess you're right about the thermostat