ClickBack:   Clickback are the market leaders when it comes to sending email messages to a purchased list.

Hotsol:  Offer Bulk Email Marketing Services for Purchased Lists or non-opt-in email lists.

Direct Aim Media: Bulk Cold Email Marketing Services

Self-Hosted:   Interspire Email Marketer or Sendy.

Or,  Google “send cold emails” to find other services. New services are appearing all the time.

Always comply with regulations governing the sending of email messages:

Do not use fraudulent transmission data such as open relays and false headers.
Do not use misleading sender or subject lines.
Add your postal address to all emails.
If you are not in contact with the recipient already include a short notice that states the email is an advertisement or solicitation.
Include a unsubscribe or opted out mechanism in every email and remove such email from your list within 10 days.