MySQL excessive tmp disk tables after Upgrade to 5.6
There are several reasons why that could be happening, and it is very difficult to point one specific cause -it could be because a change on the query optimizer, bad query statistics, parameters whose defaults changed from version to version, the changes on replication format, the data types you are handling, a change on the row format, etc.

The critical point here is to identify the differences on query execution: it would be nice if that would have been identified before the upgrade, but if you say that the master is not showing that behaviour, that may be enough. You need to discover which queries are creating those temporary tables. As you are using Percona Server 5.6, there are 2 main tools:


use the extended logging available on Percona and using pt-query-digest to identify and summary the offending queries, or
Use the performance_schema available since 5.6


Both tools can be used for identifying those bad queries. After that, you will be able to profile each query with the standard tools: EXPLAIN, the profiling metrics, the handler statistics, etc. In some cases, you may need to change the configuration, in other the queries, indexes or the structure itself of your database (for example, blobs usually cause problems because temporary tables using them cannot be on memory).

One thing that may actually be useful, independently of all of above is the replication format. If you are suffering from temporary table creation on the slave you are using STATEMENT or MIXED replication format (or your tables do not have primary keys). Row based replication, in some cases (when queries do not modify many records at the same time) may help with both query latency and avoiding slave drifting, so you should at least consider that.