You should always have a carbon monoxide tester in your home. You dont need a service man to check for a cracked heat exchanger, unless your blind.
Just check the plenum and heat exchanger for a crack, simple.
Most of these new Hi Eff furnaces are built with so many saftey devices, if something goes wrong they shut down. Then call a service man or women

.
The PC board in the furnace goes through 20 saftey checks before it even kicks on.
If the pilot or HSI doesnt start up they dont go on.
If there is no flame they dont go on.
If the blower fan doesnt start up prior to all this, they dont go on. Etcetera....
If youre going to get a new furnace or aircon put in, make sure they do a heat calculation, or your also screwed. Many times they put the wrong size in.
In the case of aircon, I have gone to service calls where the compressor is over worked or just dies early because the wrong size a/c unit was installed.
Make sure its a good company, and a seasoned guy. Half the techs out there cant diagnose a problem, theyre too stupid.
How do I know?
Try being the only female in class with a bunch of dumb borish idiotic yet hopeful service guys who cant even hold a philip screw driver correctly.
Out of a class of 30, there are usually 5 who will make good techs, the rest should find another career.