Adding "a bunch of hot water" to achieve a mash out would be a second infusion (double infusion mash). That's probably not practical for your rig.
Do what was suggested above.
Add the recommended amount of water to achieve a 147° F single infusion mash. Rest for 60 minutes.
Toward the end of the rest, heat the recommended amount of sparge water to 180° F.
Vorlauf and drain the mash/lauter tun. As the runnings go into the kettle, begin heating the wort for boiling.
When the first runnings are in the kettle, add the hot sparge water to the mash/lauter tun, stir, vorlauf, and drain again.