What is the ruling on performing tayammum for one who has had intercourse with his wife and fears falling ill from severe cold when performing ghusl for the Fajr prayer before going to work, knowing that there are bathrooms at work but the water there is cold, and is it permissible for him to combine the Dhuhr and Asr prayers at Maghrib due to his inability to perform them at their prescribed times?

You are not required to abstain from intercourse; rather, you have leeway in it at a time when you can perform ghusl (definition), even with heated water, and dry yourself before traveling. You must heat water and perform ghusl after intercourse to pray Fajr before your work. Furthermore, it is not permissible for you to miss the Dhuhr and Asr prayers until you return home; rather, you must pray them within their prescribed time.