The hottest printing temperatures?

ABS can go up to about 240 Celsius, and PLA around 190.  Printing that high is not recommended however, since these plastics can burn, clogging the nozzle if left idle at temperature for more than 10 minutes.  I normally print at 230 for ABS and 185 for PLA, but I have an E3D hot end, so those temperatures are not the temperatures which you would use on a stock Solidoodle printer.  Some filaments print better at other temperatures as well.  Some manufacturers make high-temperature PLA which needs at least 200.  Check the filament suppliers suggested temperatures to get a starting point.  If using a PEEK hot end, be extra careful not to let it get too hot and melt.

Stick some blue painters tape on there and try to use PLA whenever possible.  ABS has the occasional warping issue even on a heated bed.  Without a heated bed, anything in ABS more than about 5cm long won't remotely stick.