there are a number of possibilities. the fact that it doesn't keep up on a mild day suggests that the performance problem may be related to a freon level or possibly a starting problem. when the compressor overheats, there is an underlying cause. compressor amps, pumping capability, metering device feed, defrost function, capacitors, contactor, freon level, superheat, sub-cooling, od stat all need to be properly tested by a qualified technician. while an intermitent problem can be evasive, it sounds like you may have a solid problem that can be detected with the right tests. you may need to get a second opinion.