1996 Cavalier (base - 2.2) Running hotter than normal

Early last week my car started running a bit hotter. A few things to note; 1. the car is now heating up (according to the temp. gauge) much faster. It gets to about half way in about 3-4 minutes. Before, it would take about 10 minutes to get to half way. The temperature outside has remained about about 15-20F before and after this problem began happening.

Now, what has me concerned is my cooling fan kicks on immediately after I start the engine and never shuts off, BUT, the temp. gauge is still going up quickly and is actually going past half way slightly. My car has yet to overheat and nothing has changed to my knowledge with the car. Could it be a bad sensor?

Help would be greatly appreciated.

It could be a bad sensor. If the sensor for the PCM reads -40 degrees (max. cold / open circuit), it will command the fan on because a problem with the sensor circuit is assumed. How often does it get to -40 degrees? :). The sender for the gauge is part of the ECT sensor, so very possibly the two problems are related. To confirm this, you'll need to buy a scan tool capable of reading ECT. Given the cost of the sensor, I would personally replace it and see if the problems go away, unless you already have access to a scan tool or were planning on buying one anyway.