Temperature Spikes

I've replaced the thermostat, flushed/filled & bled (burped) the cooling system, and changed the radiator cap. Can't figure this one out ! Going down the road at normal speed (30-60 mph), the temp guage reads fairly cool. It's a '92 SC with the standard guage. When you come to a stop and idle for 1-3 minutes, the temp guage begins to climb steadily - to the point of very warm and almost hot. The fan kicks on and prevents it from over-heating - but why does it spike so high ? This car used to run way down low on the cool side - and stay there - irrespective of the temp/conditions. Now, after a drive, you can open the hood and feel/smell the heat ! My fear is that the head gaskets are going to blow. Any ideas ?

Do you still have the stock 195deg thermostat?

I'd suspect a blocked up radiator.

You may already be experiencing the beginning of headgasket failure. It would be a good idea to get the antifreeze tested for hydrocarbons.