Gauge pegs, engine gets hot, A/C quits cooling

After about ten minutes of run time, gauge goes from normal and the A/C blowing cold to gauge pegs, engine seems to get hot, A/C starts blowing hot. Coolant reservoir is filled to correct line. I let it sit overnight and it goes through the exact same timeline/process. When I run the truck at higher speeds and RPM the gauge pegs faster.

Steps to diagnose? I do not want to take it in and they start replacing one thing at a time until it is fixed.

Thanks in advance for your time!