My mazda3 2014 I brought new off the lot in 2014?

Your '14  M 3 does not even have a level indicator. Read manual.

https://owners-manual.mazda.com/gen/en/mazda3/mazd...

5 answers here assume you have any idea what you are talking about.

You don't even have an oil pressure  or head temp lite, like One insinuated.  Both are incorporated into an engine-shaped warning lite.

The blue thermometer in blue liquid  means engine not warmed up. That's why it goes out.  If you did have a level sensor, which seems  impractical as coolant constantly moving and splashing--or, should be-- will not go out, your level will not get higher.

No  hi   and lo marks, either. Just check overflow and radiator, see if liquids within 1" of top.

at least bax makes a good suggestion; no "harm" in checking  coolant level.  and  does not conclude on a car he hasn't worked on.

Pop the hood and check the coolant reservoir - it's probably just a little bit low.

There should be low and high marks on it - try to use the same kind of coolant (color) and get it between the marks.

CHECK THE COOLANT LEVEL! ou can add a SMALL amopunt of WATER and do no ham to get it UP a little bit! TEh COOLANT LEVEL switch maybe STUCK< so remvoe and CLEAN IT! Use ONLY MAZDA genuein COOLANT and NO TPRESTONE or NAOPA junk either! I LOVE the MAZDA #! They just FEEL good! USe OPENNZOIL ULTRA PLATINUM OIL and NOTHEINE ELSE! NO VALOLINE or EL CHEAPO oil changes that bring SLUDGE and TARRYWAX along with their use! PNNZOIL ULTRA is made from NATURAL GAS and CLEANS things UP as you DRIVE! Your CONVERTER and O2 sensors will last LONGEST this way and the engien will remain COOL INSIDE! POWER WASH the space BEHIND the RADIATOR a a DIY car wash HERE is where LEAVES< TWIGS< GRAS< FEATHERS< and ANIMAL Droppings have collected for YEARS! REMOVE the TIOP RADAITOR hold down to gain ACCESS if you HAVE TO! CLEAN is the NAME of the game with ANY CAR and it is a SHAME there are SO MANY BAD OIL Still on the market! INSTALL a set of DENSO TWIN TIP IRIDIUM LASER spark plugs! There is MORE power hiding in there and the IRIDIUM will GET IT OUT! You will SAVE on gas and PROTECT it from MORE sludge building! SINCE there is a BREATH HOLE in your RAD cap, it is LIKELY that some has EVAPORATED over 60,000 miles! NOTHING to get ALARMED ABOUT! if in DOUBT stop by a MAZDA dealer  and let them LOOK AT IT and TOP IT UP FOR YOU using genuine MAZDA coolant! Use AMSOIL POWER FAOM if you can FIND ANY< to clean your THROTTLE BODY and IDLE AIR CONTROL VALVE! This where teh final AIR/FUEL mixture around TOWN is done! A DIRTY IAC valve will RUIN mileage a=in stop and GO traffic! AND CAN burn your CONVERTER UP in the LONG RUN! IT should be FACTORY< SHOWROOM FLOOR CLEAN at ALL Times! ADD up to TWO CUPS of clean drinking water to see if THAT HELPS OUT! You CANNOOT harm anything by doing so!  GOOD LUCK!

Take the radiator cap off and run the motor for 15 minutes. If you have air bubbles coming out of the radiator neck you have a leak somewhere or the head gasket is bad and you are burning antifreeze.

Is it a Coolant Lite; Or; A  Blue Thermometer?

The blue  thermo  sez   you arent warmed up. That's why it Goes Out. Mine took 4 minutes, once, I checked coolant level when it cooled off. All OK.

REF: Have a 2015 Maz. 3, bought w/80K; coolant Fine, asked dealer about the "blue lite"

Check the coolant level when the engine is stone cold. If it's low, there is a leak that needs fixing. If it's full, examine the belts and the connections to the temperature sensors. When the coolant warning light comes on, park asap, determine why the light while you wait for the engine to cool. Running an overheated engine can cause mechanical damage.

Yes, add coolant if it's low. And for future reference, when the 'oil' light comes on that doesn't mean the oil is full and pressure is OK.

Check your coolant level.