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.