Sounds about right, Mij. Can you set zones on your HRM? What i do is go out slowly, glancing at monitor to check that i'm below 65% (or whatever). Set the monitor for the zone i'm heading for - say i want to do a tempo run at 85%. My tempo (to use your figures) target would be 160 bpm. so i set the zone for 157 minimum and 163 maximum. The target figure is in the middle. Then as i reach the end of the warm up i switch on the beeper and start running harder. When the beeper stops beeping, i'm in the target zone and just keep running without beeping which may require slowing or speeding up a bit depending on the levelness of the road.
(Am i making sense?) At the end, i slow down, switch off the beeper and jog the last mile home.