If I’m facing major tempo / beat changes I usually wait for a break at the first song and then try to mix in the second song there, using a part where there’s no beat at all or only some percussion that doesn’t immediately points the crowd to the fact that the tempo has changed.
Same thing if you want to go back to your original tempo, wait for a break in the current song and try to mix in the next one from there.
Try to play around a little with effects like delay and phaser, that helps me sometimes to cover the fact that the beats don’t match exactly.