Many monitors will become "tame" with a little bit of work, but some still do not become tame even after most others would've gotten used to your presence.
"Tame" is not a word to be used for monitors. A healthy monitor may tolerate you at best, but it will not allow you to just grab it. If a monitor is allowing you to just grab it, something is severely wrong. They are wild animals, and they act like it. As far as gaining their trust, do as you would with any wild animal, like say a feral cat or a wolf. Feed it and don't force anything, and eventually it will come to you, but if you try to force it, it will just hate your guts.
As far as temperatures, monitors all like hot temps. The SURFACE temperature of their basking spot should be 130 or higher for just about all monitor species, and the basking spot should evenly heat the monitor's whole body. (A bank of low wattage halogen flood bulbs works great, don't use high wattage spot bulbs.) Some monitors, especially the medium and large ones, will use basking spots up to 160 degrees surface temperature.