Heat pump backup furnace not holding set temp

Newly installed baseboard heaters (two 8 foot,1500W,240 Volt controlled by wall T-Stat). When I turn the system on and rotate T-Stat full hot she starts up, but instead of giving instant full heat she seems to go full hot, then back off and go to moderate heat and then back to full heat (before T-Stat is satisfied), is this normal? System works well (on exterior Sun Porch, but seems to take a long time to come up to full heat).

Okay, this came up while visiting Mom over Christmas; it is a return issue that was fixed (?) last year. This is a Rheem Classic IX heat pump that is about 20 years old. Still works well when it runs. Previously had an issue with the air handler fan running all the time. When the local AC guys troubleshot it they said this unit does not have a relay (already knew that because I had a peak inside to see if it had one I could replace) and the problem was a circuit board, BUT they said that particular board was a bit pricey and it was probably more cost-effective to simply let it run as otherwise it was operating fine. Think they topped off the refrigerant as well, but it was not much needed. Sometime a few months later the unit (compressor) wouldn't kick on. Enter my older brother who was visiting from out of state and had the ac guys back out. They replaced a circuit board (a little fuzzy as to whether this was the same board referred to earlier) and everything was working. Also, brother said not very expensive. Fast forward to a few days ago, noticed her house was a bit chilly and investigation revealed fan running but outside unit not. This particular unit has a reset button on the back near the line set and electrical connections. [Side note: I never knew that was there, but on a previous trouble call one of the techs had pointed it out to one of my siblings; I think that was the extent of the problem at that time. No indication on why it had tripped]. Pushed it and unit came on; good heat output inside. Outside temp warmed later in the day so I set the TS to off. That night tried for a little heat and had to again push the reset outside. Seemed like it would run one cycle but then trip, but on at least one occasion it tripped prior to reaching the set temp, maybe 5 minutes of run time. Also the following day it ran a cycle or two [I]without[/I] tripping. So, anyone hazard a guess as to what we're dealing with here (other than a 20 year old system)? Any chance the problem is in the reset itself and not something else that's making it trip? Anything DIY-checkable. :confused: