@Coding Badly, why do you feel he is better off without a crystal?
I don't have enough information to have an opinion one way or the other. Which is why my post is ambiguous... Should work well (no guarantee from the management smiley-wink). ---versus--- When in doubt, get the crystal out.
Using an external crystal does require more power. If low-power is paramount then running from the internal oscillator may be worth the risk. If reliable serial communications is paramount then running from an external crystal may be worth the extra power consumption. Only @lemming can make that decision.
If the temp variation causes a 4% change in clock frequency, and you are using a baud rate with say a 3% error at 1 MHz, I think you're going to have a problem.
That's unlikely. Hardware based serial communications has a high probability of working up to ±10% total clock error. The ±4% I recommend provides a nice cushion.
In addition, if @lemming has control of both sides he can use a zero-error baud rate.