I agree with Number 2 with everything above, when I was in University I did tempo work on treadmills and stationary bikes: The result was that my IT band had tightened up and the middle/outside quad muscles were overpowering the inside quad muscles. This lead to the patella tracking to the outside and causing and grinding the patellar tendon. I needed rehab and time away from the track.
I don’t know about HR in terms of running Tempo but I believe you can do tempo with weights. This is currently something I’m experimenting with with intensity ranging from 25 to 70% for MMA.
In regards to the weights, you have to make sure the volume is taken into consideration; as well as, the metabolic effects, recovery time, and High intensity work (sprints/weights/plyos).