A/C electric, heater gas
Absolutely not.  Merely having the pilot light on doesn't make enough heat to overheat a house.  

Your cooling problem is probably

a) Problems with the A/C unit, e.g. low refrigerant or clogged condenser. 

b) hot weather beyond the design basis of the system

c) a design basis that's too small for your tastes

d) something you are doing that's making a lot of heat.  E.g. cooking, baking, running a clothes dryer, printing on a laser printer, running a gaming PC, etc.



How do we test these things?

a) A/C problems: have the unit inspected. 

b) Extremely hot weather: check the weather history.   

c) Too small for home:  Have someone evaluate the size of the A/C that your home should have, preferably without seeing the unit you have now, as that could bias their recommendation. 

I myself prefer units "on the large side" - that way I am free to turn it off when I'm away, without worrying about it struggling to catch up when I do turn it on.  Turning it off when you're away saves a lot of energy, though many people will not admit it.  

d).  Other loads: Most are electric.  Find the electric meter.  There will be a spinning disc which changes speed based on your usage -- or a digital equivalent, that you may have to push a button or wait a few seconds to see.  Learn how to read this momentary rate of usage.  When the A/C is straining, run out and check its speed.  Then turn off the A/C and check it again.  It should nearly stop.  If it's still moving at a good clip, you are making heat inside your house, which is obviously fighting the A/C.