There is one period representation that I know of showing scale armour:

And several literary descriptions of armour albeit not very specific of the form it took. There are more statuettes IIRC showing the banded leg armour that were presumably protecting where the elephant was most vulnerable to attack.
These plus many illustrations from other periods of heavily armoured elephants (all the way up to the 18th C. in India) mean it does not look impractical to me. Perhaps less of an issue than for horses that suffer severe overheating problems in hot climates when weighed down with a heavy caparison.
It also makes a lot of sense from a point of view that the elephant was seen as a prestige symbol and directly linked with kingship in the Hellenistic world. Providing expensive armour to your battlefield command post and bling for the post-match victory parade seems quite logical.