Freezer trouble

I have a 15 year old Tappan chest freezer that is not working properly. The freezer will come on and then shut back off after a few seconds. It will come on if you tap the cold setting control and will sometimes run for hours bringing the temp back down to zero, but once it shuts off it may not come back on. If you touch the compressor after it has been running for hours it is warm but not to hot to lay your hand on. I have a feeling that the temp control may need to be replaced but would like opinions.

Thank you

Here are your parts
Parts for Frigidaire TFC13M0AW0 Freezer - AppliancePartsPros.com

Since tapping the thermostat fixes the problem I would replace it.

The turning on then off after a couple seconds is usually a start device or compressor problem but I would still lean towards the thermostat.