Air compressor does not kick in unless ambient temp is > 80

I have a window unit air conditioner and the compressor seems to only kick in when it is really hot in my bedroom. Otherwise, the fan just runs all night long. I have the thermostat set to the maximum setting yet it does not blow cold air when the ambient temp in my bedroom is in the 70's. Should I replace the thermostat? Should the air baffle be closed to disallow outside air to come in? Thanks.