The fundamental problem is that anything you do to alter the thermal environment or hydrological environment will likely result in changes in breathability by the very nature of the interlock of atmospheric mix and extant life cycles and hydrology.
(which said, if the atmosphere is already breathable, it's either replacement of native biosphere, or hydrological or thermal issues that you're trying to fix.)
To raise temps, you either have to do one or more of:
- darken the surface,
- pump vast amounts of waste heat
- release core heat to the surface faster
- alter the atmosphere by release of greenhouse gasses
- move the planet's orbit
Lets take the least disruptive to local life: waste heat. Build your fusion plants. The end result is helium, and some lithium, carbon, maybe even oxygen. No biggie, right? Well, most of the hydrogen is going to come from water. This releases a lot of oxygen. Oxygen is only useful in partial pressures between 0.1 and 0.4 atmospheres (multiply local pressure times local percent to get partial pressure); outside that range, you get issues. Below it, and you are not terribly active, or you pass out; above 0.4, and the excess O2 is toxic.
Ok, so some greenhouse gasses, instead? Most are themselves toxic to humans... Methane, Carbon Oxides (CO, CO2), Nitrogen Oxides (which combine to make acid rain, no less!)...
Core heat? (AKA Geothermal.) Can result in emissions of multiple toxic gasses in the drilling. In order to terraform using it, you also need to distribute the heat via working fluids (be they liquid or gas) - but this also raises cloud cover, increases albedo, and wrecks local weather patterns until it stabilizes. And on a useful terraforming scale, also can significantly cool the upper mantle, resulting in changes in tectonic activity.... also releasing more toxic fumes, ash, and possibly natural radioactive gasses. (OK boys and girls, Can we say 'Radon'? ... Good! I knew you could!)
Darken the surface: involves altering the plant life and/or dusting the ice caps. Alter the plant life, alter the oxygen cycle, and breathability...
Upping the pressure?
If you take a breathable 50% O2, 5% CO2, 45% N2 0.3 atmosphere, that's a PPO2 of 0.15 atm... about what very high flying pilots get on supplemental oxygen in unpressurized aircraft, BTW. Now, you want to raise it to standard with the hydrogen cracked to fuel your PP... by the time you get to the mildly toxic PPO2 0.45 Atm, you've gone only to 0.6 Atm, and the percentage is now 75% O2, 2.5% CO2, and 22.5% N2, and a PP CO2 that's low enough to cause you to forget to breath... Oh, and at 0.45ATM PPO2, your match will burn your fingers when you light it, your cigarette lighter is a blow torch, etc...
And if you actually raise the atmosphere to standard's 0.75, you're casing blindness.... at least amongst those who haven't burned themselves to death by accidental Apollo One reenactments.