After retiring as a player, Malpas assumed full-time coaching duties at Tannadice, having been acting as player/coach since 1991. He was part of the temporary management team following the dismissal of Alex Smith in October 2002, but left the club in January 2003.  He initially joined Motherwell as assistant manager to former coaching colleague Terry Butcher. Malpas became Motherwell manager in May 2006, following Butcher's departure to coach Sydney FC. He left the club in June 2007 after one season in charge, having taken the team from a comfortable mid-table position to one that narrowly avoided relegation. Malpas became caretaker manager of the Scotland under-21 team in August 2007, but missed out on the permanent position to Billy Stark.  In January 2008, Malpas became manager of Swindon Town after the takeover of the club by local businessman Andrew Fitton, replacing former Dundee United teammate Paul Sturrock. Malpas was sacked by chairman Andrew Fitton on 14 November 2008 after a poor run of results and shock exits in the FA Cup to Histon and in the Football League Trophy within a week. He joined Terry Butcher again as assistant, this time at SPL club Inverness Caledonian Thistle. In 2013, Malpas moved with Butcher to Hibernian, rejecting the chance to manage Inverness. Butcher and Malpas both left Hibernian in June 2014, after the club had been relegated from the Scottish Premiership.  Malpas became director of football at Raith Rovers on 26 December 2014. He left Raith Rovers on 22 May 2015 and was inducted to the Scottish Football Hall of Fame in October 2015.  Malpas returned to Inverness Caledonian Thistle in April 2017, working for manager Richie Foran.

Answer this question "Is there any teams he coached on full time?" by extracting the answer from the text above.
He initially joined Motherwell as assistant manager to former coaching colleague Terry Butcher.