Temperature gauge consistently below normal

[95greensvx]

I let my car warm up every morning for ten to fifteen minutes prior to leaving for work and the temperature gauge always reaches normal temp (in the middle of the gauge) but once I begin driving the temperature drops towards the bottom showing that the car is running cold. I am not sure why the engine is doing this. It will continue to run below normal as long as I am moving.

The other problem is the heat is intermittent. It decides to consistently blow out cold air when turned on if the temperature outside is below 50 degrees, if it's warmer than 50 then it will blow out warm air. Not sure if the problems are linked but I have replaced the thermostat already but maybe I got a bad thermostat?? I also have checked the lines going into and out of the heater core and the passenger side one is warm but not hot and the drivers side one is cold so I am assuming I have a clogged heater core (unfortunately) but I have flushed it various times and water comes out just fine so I am thoroughly confused as to what is going on with the temperature gauge and the lack of heat. Any ideas are appreciated. Thanks.