get_queried_object()->term_id;
OR
$taxonomy = get_queried_object();
$current_tax = $taxonomy->term_id;

Get your term details by term name based for custom taxonomy.
$term = get_term_by('name', 'metal-idols', 'prod_tax'); // replace them with correct/appropriate values

check if current taxonomy/category equals what we get in $term, then you can change dimensions for that product else go on with current dimensions.

for example :

if($current_tax == $term->term_id) {
	// These parameters will be for particular category/taxonomy
	$width = '';
	$height = '';
} else {
	$width = '';
	$height = '';
}

You can use dimensions or code in if else condition the way you need to use.