What do you call a person who repairs large electrical appliances and also electrical wiring and heating in houses?
In this day and age we seem to have a title for every possible type of occupation. You have already suggested the best titles for the occupations you mention: A man who repairs broken appliances is an appliance repairman; a person who repairs electrical wiring is an electrician. A person who works on faulty heating systems is called a heating repair contractor, while a man who works on air conditioners is called an air conditioning repair contractor. In earlier times, a man who did all of these things was generally called a handyman.