Not unless you want to risk damaging your engine.  When the temperature light comes on, it means your engine is overheating.  An engine should not overheat if the cooling system is properly filled and is working normally—even during hot weather or stop-and-go driving.  Sometimes abnormal driving conditions such as towing a heavy trailer during hot weather may overload the cooling system’s capacity to control heat, but usually a temperature warning light means trouble.

What to do:  Stop driving immediately, pull over to the side of the road, shut the engine off and wait for things to cool down.  WARNING:  Do not attempt to open the radiator!  Opening the cap could allow steam and water to blow out and burn you.  Wait at least a half hour for things to cool off before you try to open the radiator cap, and then do it slowly, going halfway to allow pressure to release, then taking it off completely.  Add water to the radiator if it is low.  Actually, you should add a 50/50 mixture of antifreeze and water, but in most cases antifreeze isn’t handy so you’ll just have to use water until you can add it later.

If you don’t stop driving…  If you keep driving an engine that is overheating, it can cause serious damage.  The engine may start to knock, which in turn can cause piston, ring and head gasket damage.  As the internal parts of the engine expand from the excessive heat, clearances may be reduced to the point where metal-to-metal contact occurs.  Valve stems may gall and stick, and the pistons and camshaft might scuff or seize.  Severe overheating also creates tremendous thermal stress in the head(s) and block.  This, in turn, may lead to cracking and/or warpage.  This is a common problem with overhead cam engines that have aluminum heads.

So, if your temperature warning light comes on, don’t ignore it!  Also, you might want to consider keeping the dash area clear of pictures and mementos so you can see all of your warning lights, it could save you a lot of time, money and headaches.