Track temp will affect the lap time as if the tyre is overheating it will lose grip resulting in slower lap times so on a hot day hards will manage much better then super softs.
Also to keep in mind the softer the tyre the quicker it degrades which also reduces grip and again slows down the lap times.
inactive managers shouldn't be able to keep up with managed teams if they are it either because there car and/or drivers are much higher levels than yours or your strategy isn't right.