Older model luxaire heatpump will blow warm air in heat mode for several minutes then star blowing out cold air. Unit has new filter and coils are clean. The blower motor. Condensing motor and compressor run but blows cold air. Any suggestions on what problem could be?

We need to know the vent temperature. You say it blows warm for a few minutes, this could be because you raised the thermostat up to many degrees and caused the second stage heat to come on. Read some of the other posts about heat pumps.