Why does STRAIGHT_JOIN consume more CPU?
According to the MySQL Documentation on JOIN Syntax

STRAIGHT_JOIN is similar to JOIN, except that the left table is always read before the right table. This can be used for those (few) cases for which the join optimizer puts the tables in the wrong order.

The comment posted suggested using EXPLAIN on both versions of the query. Based on this suggestion and the join optimizer's current behavioral settings, the output of the two EXPLAIN plans should be noticeably different. Being more specific, the order of the tables in EXPLAIN plan of the STRAIGHT_JOIN will have tables being accessed in a different order from the other EXPLAIN plan of the regular join.
OPTIONAL SUGGESTIONS
You could change the optimizer switches to change its decision making process.
You could run one of the following switch settings with your regular JOIN:
SET optimizer_switch = 'batched_key_access=off,block_nested_loop=off'; SELECT ... JOIN
SET optimizer_switch = 'batched_key_access=off,block_nested_loop=on'; SELECT ... JOIN
SET optimizer_switch = 'batched_key_access=on,block_nested_loop=off'; SELECT ... JOIN
SET optimizer_switch = 'batched_key_access=on,block_nested_loop=on'; SELECT ... JOIN

Then, you could run one of the following switch settings with your STRAIGHT_JOIN:
SET optimizer_switch = 'batched_key_access=off,block_nested_loop=off'; SELECT STRAIGHT JOIN
SET optimizer_switch = 'batched_key_access=off,block_nested_loop=on'; SELECT STRAIGHT JOIN
SET optimizer_switch = 'batched_key_access=on,block_nested_loop=off'; SELECT STRAIGHT JOIN
SET optimizer_switch = 'batched_key_access=on,block_nested_loop=on'; SELECT STRAIGHT JOIN

You could measure CPU and query performance for each of these eight(8) JOINs.
GIVE IT A TRY !!!
BTW other have good answers on STRAIGHT_JOIN

Apr 28, 2011 : Why does STRAIGHT_JOIN so drastically improve this query, and what does it mean when it is written after the SELECT keyword?
Feb 04, 2009 : When to use STRAIGHT_JOIN with MySQL