The former Scotland boss, 54, had said "it was like playing against 12 men" after Hearts lost 2-1 to Rangers in December.

His side's next game is against visitors Livingston in the Scottish Cup on 19 January.

The second part of his ban is suspended until 31 December 2019.

Scottish FA compliance officer Clare Whyte raised disciplinary proceedings regarding an alleged breach of rule 72.

The rule states that no team official shall "criticise the match officials in such a way as to indicate bias or incompetence or make remarks about such match official(s) which impinge on his character".